MILLIKAN  -  GALE  -  BISHOP 


EDUCATION  DEPT. 


A  FIRST  COURSE  IN  ;; ; 
LABORATORY  PHYSICS 


FOR  SECONDARY  SCHOOLS 


BY 


ROBERT  ANDREWS  MILLIKAN,  PH.D.,  Sc.D. 

DIRECTOR  OF  THE  NORMAN   BRIDGE   LABORATORY   OF   PHYSICS,    PASADENA,   CALIFORNIA 


HENRY  GORDON  GALE,  PH.D. 


EDWIN  SHERWOOD  BISHOP,  PH.D. 

FORMERLY   INSTRUCTOR  OF  PHYSICS  IN  THE  SCHOOL  OF  EDUCATION  AT  THE 
UNIVERSITY   OF  CHICAGO 


G1NN  AND  COMPANY 

BOSTON    •    NEW  YORK    •    CHICAGO    •    LONDON 
ATLANTA    •    DALLAS    •    COLUMBUS    •    SAN    FRANCISCO 


.->'„    :   ;  ;..;*        ,      ,      «"r 

-;\*    ,  ,f        i     .ic 

N*  »*8  »*;«»«•   ;:^s,".' 

acs? 


COPYRIGHT,  1914,  BY 

EGBERT  A.  MILLIKAN,  HENRY  G.  GALE 
AND  EDWIN  S.  BISHOP 


ALL   RIGHTS  RESERVED 
523.9 


Q»t 

EDUCATION 


gtbtnatum 


GINN   AND  COMPANY  •  PRO- 
PRIETORS  •  BOSTON  •  U.S.*. 


PREFACE 

This  course  of  about  fifty  laboratory  exercises  represents  an  endeavor  to  bring  beginning  students 
of  physics  into  direct  first-hand  contact  with  the  most  significant  of  the  principles  of  the  subject  and 
with  their  applications  to  daily  life. 

Since  the  precise  method  of  accomplishing  this  end  will  depend  upon  the  sort  of  laboratory  equip- 
ment which  is  available,  the  course  has  been  given  considerable  flexibility  by  introducing  alternative 
experiments. 

Thus,  if  gas  is  not  accessible  the  student  will  omit  Exp.  5,  but  will  get  exactly  the  same  principle 
through  performing  Exp.  5  A.  Or,  if  the  laboratory  is  not  equipped  with  commercial  ammeters  and 
voltmeters,  Exp.  31  will  be  omitted  and  Exp.  31 A  performed.  Similar  choices  will  be  found  indicated 
throughout  the  text. 

Another  feature  of  the  course  is  that  the  experiments  do  not  presuppose  any  previous  study 
of  the  subject  involved,  or  any  antecedent  knowledge  of  physics.  The  laboratory  work  may  be  kept 
in  advance  of  the  classroom  discussion  throughout  the  entire  course  if  desired.  Indeed,  in  their  own 
elementary  work  the  authors  prefer  to  let  more  than  half  of  the  experiments  constitute  the  student's 
first  introduction  to  the  subject  treated.  Furthermore,  students  are  neither  instructed  nor  advised 
to  study  their  experiments  before  entering  the  laboratory,  for  each  experiment  has  been  arranged  to 
carry  with  it  its  own  introduction. 

Problems  on  the  practical  transformations  of  energy  have  been  given  the  important  place  in  this 
course  which  they  merit,  and  it  is  hoped  that  an  advance  has  been  made  in  the  way  in  which  they 
are  treated.  Thus,  in  comparing  the  efficiencies  of  two  different  appliances  which  accomplish  the 
same  result,  as,  for  example,  an  electric  stove  and  a  gas  stove,  the  f^ct  has  often  been  overlooked  that 
in  daily  life  people  are  interested  in  efficiency  only  as  it  affects  cost  of  operation.  The  emphasis  has 
here  been  thrown,  therefore,  on  the  real  test  of  efficiency  from  the  consumer's  standpoint,  namely 
the  relative  cost  of  a  given  output  rather  than  on  the  mere  ratio  of  energy  output  to  energy  input. 

In  order  to  instil  in  the  pupil  the  habit  of  orderliness  and  to  teach  him  to  collect  and  organize 
related  data  in  such  a  way  as  to  draw  conclusions  from  it,  a  form  of  record  has  been  placed  at  the 
end  of  most  of  the  experiments.  This  procedure  also  enables  the  teacher  to  check  up  the  experiments 
with  a  minimum  expenditure  of  tune  and  energy.  In  the-tcase  of  qualitative  work  the  Record  of 
Experiment  has,  as  a  rule,  been  omitted. 

For  the  benefit  of  those  who  use  both  this  book  and  the  classroom  text  entitled  "  A  First  Course 
in  Physics,"  a  suggested  time  schedule  for  a  thirty-six  weeks'  school  year  is  inserted  in  Appendix  A. 
Whether  this  particular  schedule  is  followed  or  not,  it  seems  to  the  authors  a  matter  of  great  impor- 
tance that  each  teacher  begin  his  year  with  some  well-considered  time  schedule  before  him,  and  that 
he  plan  each  lesson  and  make  his  omissions  and  additions  with  this  schedule  in  mind.  Otherwise  it 
almost  invariably  happens  that  the  subjects  treated  in  the  first  half  of  the  text  receive  a  dispropor- 
tionate amount  of  time. 

The  initial  cost  of  equipment  for  satisfactorily  conducting  this  course  with  classes  of  say  twelve 
pupils  need  not  exceed  two  or  three  hundred  dollars.  If  commercial  electrical  instruments  are 
employed,  however,  the  cost  may  of  course  reach  a  much  higher  figure. 

R.  A.  M. 
H.  G.  G. 
E.  S.  B. 
[iii] 


fiK     ,,:, 


CONTENTS 


EXPERIMENT 


DATE 
ASSIGNED 


DATE 
APPROVED 


1.  Determination  of  TT 

2.  Volume  of  a  Cylinder 

3.  Density  of  Steel  Spheres       .... 

4.  Pressure  within  a  Liquid      .... 

5.  Pressure  in  Gas  Mains 

5  A.  Lung-Pressure 

6.  Archimedes'  Principle 

7.  Density  of  Liquids 

8.  Density  of  a  Solid  Lighter  than  Water 

9.  Boyle's  Law 

9  A.  Weight  of  Air 

10.  Molecular  Constitution  of  Matter  .     . 
10  A.  Evaporation  and  Dew-Point  .     .     . 

11.  Resultant  of  Two  Forces 

12.  The  Pendulum 

13.  Hooke's  Law 

14.  Charles's  Law 

14  A.  Gay-Lussac's  Law 

15.  Expansion  of  Brass      

16.  Principle  of  Moments 

17.  The  Inclined  Plane 

17  A.  The  Use  of  Pulleys 

18.  Heat  of  Combustion  of  Gas  .... 

18  A.  Efficiency  of  a  Gas  Stove  .... 

19.  Specific  Heat 

20.  The  Mechanical  Equivalent  of  Heat  . 

21.  Cooling  through  Change  of  State    . 

22.  Heat  of  Fusion  of  Ice 

23.  Boiling  Point  of  Alcohol 

24.  Effect  of  Pressure  on  the  Boiling  Point 

25.  Magnetic  Fields 


EXPERIMENT 


DATE 
ASSIGNED 


DATE 
APPROVED 


26.  Molecular  Nature  of  Magnetism 

27.  Static  Electrical  Effects 

28.  The  Voltaic  Cell 

28  A.  The  Voltaic  Cell 

29.  Magnetic  Effect  of  a  Current 

30.  Properties  and  Applications  of  the  Electromagnet 

31.  Electromotive  Forces 

31  A.  Electromotive  Forces 

32.  Laws  of  Resistance 

32  A.  Wheatstone's  Bridge 

33.  Internal  Resistance 

34.  Efficiency  of  Lamps 

34  A.  Heating  Effects  of  the  Electric  Current 

35.  Electrolysis  and  the  Storage  Battery 

36.  Induced  Currents 

37.  Power  and  Efficiency  of  Motors 

37  A.  Principles  of  the  Motor  and  the  Dynamo 

38.  Speed  of  Sound  in  Air 

39.  Frequency  of  a  Tuning  Fork 

40.  Wave  Length  of  a  Note 

41.  Laws  of  Vibrating  Strings 

42.  Plane  Mirrors 

43.  Index  of  Refraction 

44.  Critical  Angle  of  Glass 

45.  Concave  Mirrors 

46.  Convex  Lenses 

47.  Magnifying  Power  of  a  Convex  Lens 

48.  The  Astronomical  Telescope 

49.  The  Compound  Microscope 

50.  Prisms  and  Spectra 

51.  Photometry 
51  A.  Photometry 

Appendix  A ' 

Appendix  B 


[vi] 


LABORATORY   PHYSICS 


EXPERIMENT  1 


FIG.  1 


TO  DETERMINE  H,  THE  RATIO  OF  THE  CIRCUMFERENCE  OF  A  CIRCLE 

TO  ITS  DIAMETER 

I.  Measurements,    (a)  Measurement  of  circumference.    Scratch  a  fine  line  A  along  a  radius  of  an 
accurately  turned  disk. 

Place  A  accurately  above  some  division  B  on  the  meter  stick  (Fig.  1),  and  roll  the  disk  between 
the  thumb  and  finger  until  A  is  again  in  contact  with  the  meter  stick.  Record  the  positions  of  A  in 
centimeters,  by  noting  first  the  whole  number  of  centimeters,  then 
the  number  of  millimeters  in  the  tenths  place,  and  lastly  the 
estimated  tenths  of  a  millimeter  in  the  hundredths  place.*  The 
circumference  is  the  difference  between  this  reading  and  the  start- 
ing point. 

Starting  at  different  marks  on  the  scale,  repeat  four  times  and  take  the  average  of  the  five  trials 
as  the  circumference. 

(6)  Measurement  of  diameter.  Lay  the  disk  flat  on  the  table.  Place  the  meter  stick  on  edge 
(Fig.  2)  so  that  the  centimeter  face  is  along  a  diameter  and  so  that  some  centimeter  division  coincides 
with  one  edge  of  the  disk.  Record  the  diameter,  estimating  tenths  of  a  millimeter. 

Repeat  four  times,  measuring  different  diameters,  and  take  the  average  of  the  five  trials  as  the 
diameter. 

II.  Computation,    (a)  The  last  figure  of  each  measurement  was  estimated  and  therefore  uncertain. 
(5)  Retain    one    more    uncertain 

figure  in  the  average  than  in  the  in- 
dividual measurements. 

(c)  After  every  multiplication  or 
division  retain  the  same  number  of 
significant  figures  in  the  product  or 
quotient  that  there  are  in  that  factor 
which  has  the  smallest  number  of 
significant  figures.  The  numbers  583, 
.409,  1.03,  .00110  hare  three  significant  figures  each.  Thus,  ciphers  before  a  number  in  a  decimal 
fraction  less  than  one  are  not  significant  figures. 

(rf)  Keeping  in  mind  what  has  been  said  about  significant  figures,  compute  TT  from  your  mean 
values  of  the  circumference  and  the  diameter. 

*  Unf amiliarity  with  the  metric  system  may  make  it  seem  more  natural  to  estimate  in  halves,  thirds,  or  quarters,  but  it 
will  be  easy  to  express  the  result  in  tenths  if  one  reflects  that  .4  is  a  little  less  and  .6  a  little  more  than  .5,  or  1/2  ;  .2  a  little 
less  and  .3  a  little  more  than  .25,  or  1/4 ;  .1  a  little  less  than  .2,  or  1/5,  etc. 

[1] 


Correct  method  of  using 
meter  stick 


FIG.  2 


Incorrect  method  of  using 
meter  stick 


EXPERIMENT  1    (Continued) 


III.  Per  cent  of  error.    The  per  cent  of  error  in  any  product  or  quotient  can  best  be  illustrated  by 
an  example.    If  in  the  measurements  -  rr-r 


=2000  an  error  of 


were  made  in  the  200, 


202  x  1005 

4-  .5%  in  the  1000,  and  -  .5%  in  the  100,  the  result  would  be  --  ^-=  --  =  2040  +.  Thus  we  see  that 

yy.o 

the  result  2040  is  40,  or  2%,  larger  than  the  true  value  2000.  We  also  see  that  in  this  case  the 
errors  1%,  .5%,  and  .5%  added  together  produce  a  total  error  of  2%.  Thus,  to  find  the  error  of 
any  experimental  result  which  is  obtained  by  taking  the  product  or  quotient  of  several  physical 
measurements,  add  the  per  cents  of  error  in  each  of  the  factors  entering  into  such  product  or  quotient, 
and  the  sum  of  these  will  be  the  per  cent  of  error  allowable  in  the  final  result.  To  find  the  per  cent 
of  error  in  any  one  of  the  factors,  find  what  per  cent  the  probable  error  in  measuring  that  quantity  is 
of  the  quantity  itself. 

Answer  in  your  notebook  the  questions  which  appear  at  the  end  of  the  experiment. 

Questions,    a.  What  per  cent  of  error  would  have  been  introduced  into  the  diameter  by  an  error 
of  .01  cm.  ? 

b.  What  per  cent  of  error  would  have  been  introduced  into  the  circumference  by  an  error  of  .02  cm.  ? 

c.  Your  value  of  TT  might  reasonably  be  in  error  by  the  sum  of  these  two  errors.    State,  therefore, 
whether  your  result  is  as  accurate  as  reasonably  careful  measurements  would  give. 


RECORD  OF  EXPERIMENT 


TRIAL 

DlAMKTEB 
IN  CM. 

CIRCUMFERENCE 
IN  CM. 

1 

2 

3 

4 

5 

Mean  = 

Mean  = 

circumference 


diameter 

Correct  value             =  3.1416 
Difference,  or  error  = 

f*rrf 

Per  cent  of  error       = 


a  1%  error      .0314 


[2] 


EXPERIMENT  2 


HOW  TO  FIND  THE  VOLUME  OF  A  CYLINDER 

I.  By  computation  from  linear  measurements,    (a)  Measurements.    With  a  meter  stick  measure  to 
tenths  of  a  millimeter  three  different  depths  of  the  cylindrical  vessel  shown  in  Fig.  8. 

Measure  the  inside  diameter  D  as  in  Exp.  1  (see  Fig.  2). 

Take  the  above  measurements  with  a  vernier  caliper,*  if  available.  2 

(5)    Computation.   Volume  of  cylinder  =  area  of  base  x  depth,  or  volume  =  — —  •  L  =  irR^L  where 
R  is  the  radius  and  L  is  the  depth.   Before  computing  read  carefully  Exp.  1,  II. 
In  this  experiment  make  all  computations  a  part  of  the  final  record. 

Questions,    a.  If  the  measured  diameter  of  a  circle  is  10.1  cm.,  and  the  true  diameter  is  10  cm.,  what  will 
be  the  per  cent  of  error  in  the  area  of  the  circle  ? 

b.  What  per  cent  of  error  will  be  introduced  into  the  computed  value  of  the  area  of  a  circle,  if  there  is 
an  error  of  0.3  per  cent  in  the  measurement  of  the  diameter  ? 

c.  Allowing  .01  cm.  error  in  the  mean  values  of  D  and  L,  find  the  per  cent  of  error  in  the  volume. 

II.  By  weight  of  water  contained  by  cylinder,    (a)    Weighing  cylinder  by  method  of  substitution. 
Place  the  empty  cylinder  with  its  ground-glass  cover  on  the  pan  B  (Fig.  3)  of  the  balance  and  add 
to  pan  A  any  convenient  objects,  such  as  pieces  of  iron,  shot,  and  bits  of 

paper,  until  the  pointer  stands  opposite  the  middle  mark  at  s,  the  rider 
R  being  at  zero. 

Then  replace  the  cylinder  and  its  cover  by  weights  from  the  set  in  the 
following  way.  Find  by  trial  the  largest  weight  which  is  not  too  large, 
and  place  it  on  pan  B.  Add  the  equal  weight,  or,  if  there  is  no  equal, 
the  next  smaller  one,  if  it  is  not  too  heavy ;  add  again  the  equal  or  next 
smaller  weight,  and  so  on,  always  working  down  from  weights  which  are 
too  large.  This  saves  the  delay  and  annoyance  caused  by  adding  a  large 
number  of  small  weights  and  at  last  finding  that  their  sum  is  still  too  small. 

When  a  balance  has  been  obtained  to  within  10  g.,  slide  the  rider  R 
along  the  graduated  beam  until  the  pointer  stands  opposite  the  middle  mark  at  8.  The  weight  of  the 
body  is  then  the  sum  of  the  weights  on  the  pan  plus  the  reading  of  the  left  edge  of  the  index  R  on  the 
graduated  beam.  Since  each  division  of  the  scale  on  the  beam  represents  one  tenth  of  a  gram,  by 
estimating  to  tenths  of  a  division  we  can  obtain  the  weight  by  this  method  to  hundredths  of  a  gram. 

*  The  vernier  is  a  device  for  measuring  fractional  parts  of  a  scale  division.  It  consists  of  a  movable  scale  AB  arranged  to 
slide  along  a  fixed  scale  CD  (Fig.  4).  The  object 
to  be  measured  is  placed  between  the  jaws  EF,  e  f 

which  are  so  made  that  when  they  are  in  con- 
tact the  zero  of  the  sliding  scale  is  opposite  the 
zero  of  the  fixed  scale.  Ten  divisions  of  the  slid- 
ing scale  AB  are  made  equal  to  nine  divisions, 
that  is,  9  mm.,  on  the  main  scale  CD ;  hence 
one  vernier  division  is  equal  to  .9  mm.  Fig.  5  (1) 
shows  the  vernier  scale  and  the  fixed  scale 
enlarged.  Here  the  zero  of  the  vernier  is  ex- 
actly opposite  the  5-mm.  mark  of  the  fixed 
scale,  this  being  the  relative  position  of  the  two 
scales  when  an  object  5  mm.  in  diameter  is 
placed  between  the  jaws.  Since  one  division 
on  AB  is  equal  to  only  .9mm.,  while  one  divi- 
sion on  CD  is  equal  to  a  whole  millimeter,  it 
follows  that  the  mark  1  of  the  sliding  scale  AB 

is  .1  mm.  behind  the  mark  6  of  the  fixed  scale  ;  2  on  AB  is  .2  mm.  behind  7  on  CD ;  3  is  .3  mm.  behind  8  ;  7  is  .7  mm.  be- 
hind 12,  etc.   Therefore,  if  the  sliding  scale  were  moved  up  so  as  to  bring  its  mark  1  opposite  the  mark  6  on  the  fixed  scale, 

[3] 


FIG.  3 


EXPERIMENT  2   (Continued) 

This  method  of  substitution  is  the  rigorously  correct  method  of  making  a  weighing. 

(6)  Weighing  cylinder  by  usual  method.  Remove  the  weights  from  pan  J5,  keeping  all  of  these  weights 
together  for  this  weighing  also.  Empty  pan  A,  move  R  to  its  zero  point,  and  bring  the  pointer  to  the 
middle  mark  by  altering,  if  necessary,  the  nut  n  (Fig.  3).  Then  place  the  object  on  pan  A  and  the 
weights  used  in  (a)  on  pan  B  and  again  bring  the  pointer  to  the  middle  mark  by  using  the  rider  R 
as  before.  Unless  the  difference  in  the  two  weighings  is  larger  than  one  or  two  tenths  of  a  gram, 
you  may  henceforth  use  the  second,  or  usual,*  method  of  weighing ;  for  the  imperfections  in  inexpen- 
sive commercial  weights,  such  as  we  are  using,  are  likely  to  amount  to  as  much  as  a  tenth  of  a  gram. 
It  was  for  this  reason  that  precisely  the  same  weights  were  used  in  both  (a)  and  (5). 

(c)  Weighing  cylinder  full  of  water.  Next  fill  the  cylinder  with  water  and  place  the  cover  over  it, 
taking  care  that  no  air  bubbles  are  left  inside.  Carefully  wipe  all  moisture  from  the  outside  and  weigh. 

Refill  the  cylinder  and  repeat  this  last  weighing  in  order  to  see  how  closely  two  observations  can 
be  made  to  agree.  From  the  mean  of  these  two  weighings  and  the  mean  of  the  weighings  of  the  empty 
cylinder  and  cover  find  the  weight  of  the  water. 

Since  1  cc.  of  water  weighs  1  g.,  volume  in  cubic  centimeters  equals  weight  of  contained  water 
in  grams. 

Questions,  a.  What  per  cent  of  error  would  an  error  of  .2  g.  in  the  weight  of  the  water  alone  introduce 
into  your  last  measurement  of  the  volume  ? 

b.  Is  your  per  cent  of  difference  in  I  and  II  greater  or  less  than  the  sum  of  the  errors  mentioned  in  I, 
Question  c,  and  in  II,  Question  a? 

c.  Do  your  results  in  I  and  II  agree  as  well  as  they  should  ? 

RECORD  OF  EXPERIMENT 

First  Observation             Second  Observation          Third  Observation                       Mean 
I.  Depth  of  cylinder  =..... cm cm cm cm. 

Inner  diameter  of  cylinder  = cm cm cm cm. 

Volume  =  ^  •  L  =  TrR*L  = cc. 

By  Substitution  By  Usual  Method  Mean 

II.  Weight  of  empty  cylinder  and  cover         = g.  g.  g. 

Weight  of  cylinder  +  water,  first  trial       =  g. 

Weight  of  cylinder  +  water,  second  trial  =  g.  g. 

Weight  of  water  alone  =  g. 

.-.  volume  of  cylinder  =  cc. 

Per  cent  of  difference  between  I  and  II    = difference _ 

1%  of  either  result 

its  zero  mark  would  move  up  .1  mm.  beyond  6.    If  the  vernier  had  moved  up  until  its  5  mark  were  opposite  10  on  CD,  the 

zero  mark  would  have  moved  .5  mm.  beyond  5,  etc.    In  general,  then,  it  is  only  necessary  to  observe  which  mark  on  the 

sliding  scale  AB  is  directly  opposite  a  mark  on 

CD,  in  order  to  know  how  many  tenths  of  a  mil-  (1)  (2) 

limeter  the  zero  mark  of  AB  has  moved  beyond      Co  i  t  3  »  5  «  ?  a  9  K>  n  »  a  *  a  it  » D          Co  _>  t  >  *  s  «  ?  g  9  .0  ..  <;  n  D 

the  last  division  passed  on  CD.   Thus  the  reading         I  I  I  I 


JJ  I  I  I  1. 1. 1. 1. 


I  1 1 1 1 1 


in  Fig.  5  (2)  is  3.7  mm.  (.37  cm.),  since  the  zero  f ,  _, 

mark  of  the  vernier  has  passed  the  3-mm.  mark " 

on  the  fixed  scale  CD,  and  the  7  mark  on  the  ^IG'  5 

vernier  is  directly  opposite  some  mark  of  CD. 

*  The  usual  method  would  be  as  correct  as  the  method  of  substitution,  provided  we  could  know  that  the  two  balance  arms 
are  of  exactly  the  same  length  (see  Principle  of  Moments,  p.  41).  If,  therefore,  you  get  different  results  by  this  method  and  the 
method  of  substitution,  you  may  know  that  the  instrument  maker  did  not  succeed  in  getting  the  balance  arms  quite  equal  in 
length.  Errors  due  to  this  cause  are,  however,  usually  very  slight. 

[4] 


EXPERIMENT  3 


FIG.  6 


HOW  TO  FIND  THE  DENSITY  OF  STEEL  SPHERES 

I.  From  weights  and  diameters  of  spheres,  (a)  Diameters  of  spheres.  Measure  the  diameters  of 
several  steel  spheres  with  the  micrometer  caliper,*  if  this  instrument  is  available.  If  not,  the  diameters 
may  be  obtained  by  placing  the  balls  between  two  blocks,  as  in- 
dicated in  Fig.  6,  and  measuring  the  distance  between  the  blocks. 
If  this  method  is  used,  however,  it  will  be  better  to  place  six  or 
eight  balls  in  a  row  between  two  meter  sticks,  set  the  blocks  at  the 
ends  of  the  row,  and  divide  the  distance  between  the  blocks  by  the 
number  of  balls.  It  will  be  best  to  use  balls  about  2  cm.  in  diameter.  Take  the  mean  of  five  or, 
better,  ten  diameter  measurements. 

Compute  the  volume  of  a  sphere  from  the  relation  V  —  \  7rJ>8,  where  V  represents  the  volume  and 
D  the  diameter. 

Remember  that  you  are  to  retain  in  any  product  or  quotient  the  same  number  of  significant 
figures  as  there  are  figures  in  the  least  accurate  factor  which  enters  into  the  product  or  quotient. 

The  following  illustrates  the  method  of  computation : 

D  =  1.9053  cm.  JD?  =  3.6302  7)8  =  6.9166 


1.9053 
57159 
95265 
171477 
19053 
D^  3.6302 

/.  volume  =  3.6215  cc. 


1.9053 
108906 
181510 
326718 
36302 


=  6.9166 


5=  .5236 

D 

414996 
207498 
138332 
345830 


3.6215 


(£)    Weight  of  balls.    Weigh  together  on  the  balances  all  the  balls  measured. 

Compute  the  density  of  steel ;  that  is,  the  number  of  grams  in  1  cc. 

II.  From  weight  of  spheres  and  weight  of  water  which  they  displace.  Fill  a  cylindrical  vessel, 
holding  about  150  cc.,  with  water  and  cover  with  a  ground-glass  plate  (Fig.  8),  carefully  excluding 
all  air  bubbles.  Dry  the  outside  and  place  on  the  left  pan  of  the  balance.  Place  on  the  same  pan, 
beside  the  vessel  of  water,  the  same  number  of  balls  used  in  I,  and  find  the  weight  of  the  whole  load. 

*  In  the  micrometer  caliper  (Fig.  7)  the  divisions  upon  the  scale  c  correspond  to  the  distance  between  the  threads  of  the 
screw  s.  This  distance  is  usually  a  half  millimeter.  Hence  turning  the  milled  head  h  through  one  complete  revolution  changes 
the  distance  between  the  jaws  ab  by  exactly  one-half  millimeter,  and  turning  h  through  one  fiftieth  of  a  revolution  changes  the 
distance  between  06  by  ^  x  \ -  =  .01  mm.  If,  then,  there 

are  fifty  divisions  upon  the  circumference  of  d,  each  divi-        . . 

sion  represents  a  separation  of  .01  mm.  of  6  from  a.  * 

To  make  a  measurement,  turn  up  the  milled  head  h 
(Fig.  7)  until  the  jaws  06  are  in  contact,  that  is,  until  the 
milled  head,  held  with  light  pressure  between  the  thumb 
and  finger,  will  slip  between  the  fingers  instead  of  rotat- 
ing further.  Never  crowd  the  threads.  The  zero  of  the 
graduated  circle  should  now  coincide  with  the  line  ec  on 
the  scale.  If  this  is  not  the  case,  have  the  instructor 
adjust  the  stop  a. 

Insert  the  object  to  be  measured  between  the  jaws  ab 
and  again  turn  up  the  milled  head  until  it  slips  between 

the  fingers  when  held  with  the  same  pressure  as  that  used  to  test  the  zero  reading.  Read  the  whole  number  of  millimeters 
and  half  millimeters  of  separation  of  the  jaws  upon  the  scale  ec  and  add  the  number  of  hundredths  of  a  millimeter  registered 
upon  d.  This  is  the  thickness  of  the  object. 

[5] 


FIG.  7 


EXPERIMENT  3   (Continued) 


Remove  the  vessel  of  water,  lift  off  the  cover,  and  drop  the  balls  into  the  water.    Replace  the 
cover,  dry  the  outside  of  the  cylinder,  replace  it  on  the  balance  pan,  and  weigh  again.    From  the  two 
weighings  find  the  weight  of  the  water  displaced  by  the  balls.    Since  1  cc.  of  water  weighs  1  g.,  this 
last  weight  is,  of  course,  the  volume  in  cubic  centimeters  of  the  displaced  water,  and 
this  is,  of  course,  the  same  as  the  volume  of  the  balls.    Take  the  weight  of  the  balls 
alone  from  I  and  compute  the  density  of  steel.     Find  the  per  cent  of  difference 
between  this  value  and  that  obtained  in  I. 

Questions.  An  error  of  .005  mm.  in  the  mean  diameter  of  the  balls  (see  illustration  in  I) 
would  introduce  an  error  into  the  diameter  of  '-r^  %,  or  .026%,  and  into  the  volume 
(^lA  of  3  x  .026%,  or  .078%. 


FIG.  8 


An  error  of  .2  g.  in  the  weight  of  the  water  displaced  by  ten  balls  would  introduce  an  error  into  the 

2 

weight  of  the  displaced  water,  and  therefore  into  the  determination  of  their  volume  of  -^  %,  or  .56%. 

.00 

a.  Using  your  own  data  and  allowing  the  same  errors  as  above,  compute  the  per  cent  of  error  in  deter- 
mining the  volume  of  the  balls  by  both  methods.    Which  method  is  the  more  accurate  ? 

b.  How  could  you  find  the  volume  of  the  ten  balls  with  a  graduate  ? 

c.  Would  this  method  (by  use  of  the  graduate)  be  as  accurate  as  the  method  of  displacement  of  water 
in  II  ?  Give  reason  for  your  answer. 


RECORD  OF  EXPERIMENT 


I. 


BALL 

DIAMETER 
IN  MM. 

BALL 

DIAMETER 
IN  MM. 

1 

6 

2 

7 

3 

8 

4 

9 

5 

10 

Volume  of  1  ball  =  \  *DS  = cc. 

Weight  of  10  balls  = g. 

.-.  weight  of  1  ball  = g. 

.•.  density  of  steel  = g.  per  cc. 


Mean  Diameter  = mm. 

= cm. 

II.  Weight  of  10  balls  +  cylinder  full  of  water 
Weight  of  10  balls  in  cylinder  full  of  water 
Weight  of  water  displaced  by  balls 
.-.  volume  of  10  balls 
Weight  of  10  balls  alone  from  I 
.-.  density  of  steel 

Per  cent  of  difference  between  two  values  of  density  given  above  = 


difference 


1%  of  either  value 


•g- 
g- 
cc. 

•g- 

.  g.  per  cc. 


[6] 


EXPERIMENT  4 


HOW  PRESSURE  BENEATH  THE  FREE  SURFACE  OF  A  LIQUID  VARIES  WITH  DEPTH 

I.  Verification  of  the  law  of  depths  and  densities,    (a)  Measurements  in  water.    Immerse  the  manom- 
eter M  of  Fig.  9  to  the  greatest  depth  possible  in  the  long  glass  vessel  V  filled  with  water.*  A  length 
of  at  least  1  m.  is  desirable  (see  tube  of  Exp.  40). 

Record  the  surface  reading  where  the  level  of  the  liquid  touches  the  meter  stick.  (Read 
where  the  level  strikes  the  meter  stick  and  not  the  point  up  to  which  the  water  laps  upon  the  K~ 
meter  stick.)  Then  record  the  level  of  the  mercury  both  in  the  open  arm  of  the  manometer 
and  in  the  arm  against  which  the  liquid  pressure  acts.  (In  the  last  two  readings  be  careful 
to  hold  the  eye  so  that  the  line  of  sight  is  at  right  angles  to  the  meter  stick,  then  take  the 
reading  at  the  top  of  the  curved  mercury  meniscus,  estimating  the  reading  to  tenths  of  a  milli- 
meter.) Evidently  the  depth  is  the  difference  between  the  first  and  third  readings,  and  the 
pressure  in  centimeters  of  mercury  is  the  difference  between  the  second  and  third  readings. 

Raise  the  manometer  about  10  cm.  and  make  similar  measurements.   Continue  in  this  way, 
raising  the  manometer  about  10  cm.  at  a  time,  until  a  depth  of  10  or  15  cm.  is  reached. 

(6)  Measurements  in  gasoline.    Fill  the  vessel  V  with  gasoline  instead  of  with  water  and 
make  a  similar  set  of  observations  for  gasoline. 

II.  Algebraic  or  analytic  representation  of  a  direct  proportion.    From  your  data  it  will  be 
seen  that  within  the  experimental  error  the  result  obtained,  for  any  liquid,  by  dividing  the 
depth  H  by  the  pressure  P  is  always  the  same,  or,  stated  algebraically, 


rr 

etc.,  or  —  =  constant. 


FIG.  9 


H 


Hence  in  the  equation  —  =  constant,  if  //  is  made  2,  3,  4,  etc.  times  as  great,  P  will  also  be  2,  3,  4. 

H  v  " 

etc.  times  as  large,  since  their  ratio  —  remains  unchanged. 

Whenever  two  quantities,  such  as  H  and  P  above,  vary  in 
such  a  way  that  doubling  one  doubles  the  other,  trebling  one 
trebles  the  other,  etc.,  the  one  is  said  to  be  directly  propor- 
tional to  the  other,  or  to  vary  directly  with  the  other. 

The  first  equation  for  a  direct  proportion  may  also  be  stated 

-p  TT  T>  TT 

by  —  =  — - »  —  =  — - »  etc.,  or  again  by  P  oc  H,  where  oc  is  read 

P2          H2       PS          HS 

"  is  proportional  to." 

III.  Graphical  representation  of  a  direct  proportion.    That    §  10 

• 

the  pressure  in  any  liquid  is  directly  proportional  to  the  depth    g 
is  shown  graphically  by  Fig.  10.    The  curve,  or  "  graph,"  for 
a  direct  proportion  is  seen  to  be  a  straight  line. 

On   a   sheet   of   coordinate   paper  plot  your   own   data. 
Choose  a  scale  along  OX,  that  is,  to  the  right  of  the  origin  0, 
so  that  the  greatest  depth  will  come  near  the  right  side  of  the 
page.    (For  example,  the  greatest  depth  plotted  in  Fig.  10  was  60  cm.  in  gasoline.)   Choose  a  different 
scale  along  0  Y,  that  is,  above  the  origin,  so  that  the  greatest  pressure  will  come  at  least  halfway  to 

*  A  piece  of  glass  tubing  about  1  m.  long  and  4  or  5  cm.  in  diameter,  closed  at  the  bottom  with  a  rubber  stopper,  answers 
the  purpose  admirably. 

Use  ^-in.  tubing  for  manometer.    Support  at  10  cm.  intervals  with  knitting  needle  K. 

m 


aao 

«tH 
O 

22.5 

•|  2-° 

1    A 
o 

a  1.5 


10 


20  C  30        40       50 
Depths  in  centimeters 

FIG. 10 


60      70 


EXPERIMENT  4   (Continued) 

the  top  of  the  sheet  of  paper.  In  general,  choose  the  scale  in  each  case  so  that  the  greatest  distance 
along  OX  (abscissa)  and  the  greatest  distance  along  0  Y  (ordinate)  are  roughly  of  the  same  magnitude. 
Then  a  single  point  will  represent  a  set  of  readings  for  a  given  depth,  the  distance  the  point  is  to  the 
right  of  0  representing  the  depth,  and  the  distance  it  is  above  0  representing  the  pressure.  Having 
plotted  all  of  these  points  for  the  set  of  data  on  water,  with  a  sharp  pencil  and  straightedge  draw  a 
line  through  0  which  passes  as  close  as  possible  to  all  of  the  plotted  points,  leaving  half  the  points 
on  either  side  of  the  line  in  case  the  line  does  not  pass  through  all  of  them.  This  is  a  graphical  way 
of  averaging. 

Questions,    a.  Why  must  the  straight  line  be  drawn  through  0,  the  origin  ? 

b.  Using  the  same  scale,  plot  the  readings  for  gasoline  on  the  same  sheet  of  coordinate  paper,  and  draw 
the  graph  showing  the  relation  between  depth  and  pressure  in  gasoline. 

c.  From  your  graph  find  (a)  the  pressure  in  centimeters  of  mercury  at  a  depth  of  40  or  50  cm.  in  gaso- 
line, (&)  at  the  same  depth  in  water.   Divide  the  pressure  thus  obtained  for  gasoline  by  that  for  water  at  the 
same  depth.    This  result  gives  the  density  of  gasoline,  which  is  about  .74.    Why  ? 

d.  The  density  of  mercury  is  13.6.    How  would  the  pressure  in  mercury  compare  with  the  pressure  in 
water  at  the  same  depth  ? 

e.  How  would  the  height  of  a  column  of  water  compare  with  the  height  of  a  column  of  mercury  which 
produced  the  same  pressure  ? 

/.  How  would  the  height  of  a  column  cf  gasoline  compare  with  the  height  of  a  column  of  mercury 
which  produced  the  same  pressure  ? 

g.  Compare  your  answers  to  the  last  two  questions  with  the  results  obtained  by  dividing  depth  by  pres- 
sure in  both  cases.  (See  data.) 

h.  How  does  the  pressure  at  the  water  taps  vary  on  going  from  the  basement  to  the  second  floor  of 
your  house  ? 

i.  Which  of  these  locations  would  be  the  better  for  the  installation  of  a  water  motor  ? 

RECORD  OF  EXPERIMENT 

(Record  the  readings  in  centimeters,  estimating  tenths  of  a  millimeter) 

WATER 


SURFACE 
READING 

OPEN  AKM  OF 
MANOMETER 

LOWER  ABM  OF 
MANOMETER 

DEPTH 

PRESSURE  IN  CM. 
OF  MERCURY 

DEPTH 

PRESSURE 

GASOLINE 


[8] 


EXPERIMENT  5 


WHAT  IS  THE  PRESSURE  OF  THE  GAS  IN  YOUR  CITY  GAS  MAINS  ? 


A 


D 

About 
50  or  60  cm, 


About 
20cm, 

v 


FIG.  11 


I.  Density  of  gasoline  used  in  manometer,    (a)  By  specific-gravity  bottle.    Weigh  any  glass-stoppered 
bottle  of  about  200  cc.  capacity  (or,  instead,  a  specific-gravity  bottle). 

Fill  with  water  and  weigh. 

Rinse  with  a  little  gasoline,  then  fill  with  gasoline  and  weigh. 

Divide  the  weight  of  the  gasoline  alone  by  the  weight  of  the  water 
alone  to  get  the  specific  gravity  of  gasoline ;  that  is,  the  ratio  of  the  weight 
of  gasoline  to  the  weight  of  an  equal  volume  of  water. 

This  is  numerically  equal  to  the  density  of  gasoline  in  grams  per  cubic 
centimeter,  since  1  cc.  of  water  weighs  1  g. 

(b)  By  balancing  columns.  Bend  a  piece  of  glass  tubing  from  5  to 
10  mm.  in  diameter  and  about  2  m.  long,  as  shown  in  Fig.  11. 

Pour  gasoline  into  the  left  arm  to  a  depth  of  10  or  15  cm.  Then  pour 
water  into  the  right  arm  until  the  level  at  C  is  3  or  4  cm.  below  the 
bend  at  E. 

Then  pour  gasoline  again  into  the  left  arm  until  the  level  at  B  is  3  or  4  cm.  below  the  bend  at  K 

Repeat  these  operations  until  the  left  tube  is  nearly  filled  with  gasoline.  (It  is  unnecessary  to 
have  any  two  of  the  surfaces  at  the  same  level  when  ready  for  use.) 

The  pressure  on  the  confined  air  in  the  bend  E  is  equal  to  the  pressure  due  to  the  column  of 
gasoline  AB  +  atmospheric  pressure  and  is  also  equal  to  the  pressure  due  to  the  column  of  watei* 
CD  -f-  atmospheric  pressure. 

Hence  the  pressure  due  to  the  column  AB  equals  the  pressure  due  to  the  column  (7D,  or 

AB  .  dg  =  CD  •  du  =  CD  .  1 

where  dg  and  dw  refer  to  the  densities  of  gasoline  and  water 
respectively. 

With  a  meter  stick  measure  AB  and  CD  and  compute  the 
density  of  gasoline. 

II.  Measurement  of  pressure  in  gas  mains.    With  a  Y  or  T 
connector  attach  the  manometers  of  Fig.  12  to  a  gas  cock. 

Open  the  gas  cock,  and  with  a  meter  stick  measure  the  height 
of  A,  £,  C,  and  D  above  the  table.    Then,  as  before, 


p  =  AB.dg=CD.dw 

where  p  is  the  pressure  in  grams  per  square  centimeter 
in  the  gas  mains  in  excess  of  atmospheric  pressure. 

Using  the  average  of  the  density  of  gasoline  as 
found  in  I,  (a)  and  I,  (5),  compute  the  pressure  in  the 
gas  mains  as  given  by  each  manometer. 

Questions,    a.  If,  in  the  apparatus  of  Fig.  11,  mercury  were  used  in  the  left-hand  arm  in  place  of  gaso- 
line, how  would  the  vertical  distance  DC  compare  with  the  vertical  distance  AB  ? 

b.  If  the  manometer  tubes  of  Fig.  12  had  had  different  diameters,  would  the  result  have  been  different  ? 
State  reasons. 

c.  Gas  plants  use  water  manometers  at  distributing  stations,  and  in  this  country  the  pressure  is  usually 
read  in  inches  of  water.    What  is  meant  then  by  a  gas  pressure  of  7  in.  ? 


FIG.  12 


EXPERIMENT  5  (Continued) 
RECORD  OF  EXPERIMENT 


I.  Density  of  gasoline 

(a)  Weight  of  bottle 

Weight  of  bottle  +  water 
Weight  of  bottle  +  gasoline 
.•.  weight  of  water  alone 
.-.  weight  of  gasoline  alone 
.-.  density  of  gasoline 

(&)  From  table  to  A 
From  table  to  B 
From  table  to  C 
From  table  to  D 

.-.  density  of  gasoline 

.-.  average  density  in  (a)  and  (b)  = 


II.  Pressure  in  gas  mains 

Gasoline  Manometer 

From  table  to  A  =  cm. 

From  table  to  B  = cm. 

.-.  AB  = cm. 

.-.  p  =  AB  •  <lg      =  g.  per  sq.  cm. 


cm. 

cm. 

cm. 

cm. 

....) 

g.  per  cc. 


AB  = 


CD=...  ...cm. 


g.  per  cc. 


Water  Manometer 
From  table  to  C  = cm. 

From  table  to  D  = cm. 

.-.  CD  =  cm. 

.•.  p  =  CD  •  1        = g.  per  sq.  cm. 


[10] 


EXPERIMENT  5  A 


HOW  MUCH  LUNG-PRESSUKE  CAN  YOU  EXEKT? 

I.  Density  of  mercury  used  in  manometer,    (a)  By  specific-gravity  bottle.    Weigh  a  glass-stoppered 
bottle  of  25  or  50  cc.  capacity. 

Fill  with  mercury  and  weigh. 

Fill  with  water  and  weigh. 

Rinse  the  bottle  with  a  little  alcohol  and  then  with  a  little  ether  to  remove  water  which  clings  to 
the  inside  before  putting  it  away. 

Divide  the  weight  of  the  mercury  alone  by  the  weight  of  the  water  alone  to  get  the  specific  gravity 
of  mercury ;  that  is,  the  ratio  of  the  weight  of  mercury  to  the  weight  of  an  equal  volume  of  water. 

This  is  numerically  equal  to  the  density  of  mercury  in  grams  per  cubic  centimeter,  since  1  cc.  of 
water  weighs  1  g. 

(ft)  By  balancing  columns.  Pour  mercury  to  a  depth  of  about  10  cm.  into  the  left  arm  of  the 
apparatus  shown  in  Fig.  11. 

Then  pour  water  into  the  right  arm  till  nearly  filled. 

The  pressure  on  the  confined  air  in  the  bend  E  is  equal  to  the  pressure  due  to  the  column  of  mer- 
cury AB  +  atmospheric  pressure,  and  is  also  equal  to  the  pressure  due  to  the  column  of  water 
CD  +  atmospheric  pressure. 

Hence  the  pressure  due  to  the  column  AB  equals  the  pressure  due  to  the  column  CD,  or 

AB.dm=CD.dw, 

where  dm  and  dw  refer  to  the  densities  of  mercury  and  water  respectively. 

With  a  meter  stick,  measure  carefully  the  vertical  distances  AB  and  CD  and  compute  from  these 
measurements  the  density  of  mercury. 

II.  Measurement   of   lung-pressure.     Arrange  a  pressure   gauge,  or  manometer,  as  in  Fig.  13. 
Record  the  level  of  the  mercury  in  arm  A  of  the  manometer. 

Then  blow  steadily  for  two  or  three  seconds  on  the  mouthpiece*  M,  and 
while  doing  so  observe  again  the  level  of  the  mercury  in  arm  A,  reading  both 
times  at  the  upper  edge  of  the  curved  mercury  surface  in  the  tube. 

Caution.  Avoid  taking  a  reading  due  to  a  quick,  hard  blow  at  Jf,  as  the 
inertia  of  the  mercury  in  the  tube  will  carry  it  higher  than  your  lung-pressure 
will  sustain  it,  and  thus  give  an  erroneous  value  of  the  pressure  which  you  are 
able  to  exert  with  your  lungs. 

Evidently  your  lung-pressure  expressed  in  centimeters  of  mercury  is  twice 
the  difference  between  the  two  observed  readings.  Why  ?  Let  h  represent  this 
pressure  in  centimeters  of  mercury. 

Compute  the  pressure  in  the  different  units  suggested  in  the  data  record, 
using  the  density  of  mercury  obtained  in  I,  (a). 

Questions,  a.  If  the  tube  A  were  several  times  as  large  in  diameter,  would  the  same  lung-pressure 
produce  the  same  difference  of  level  between  the  two  sides  of  the  manometer  ? 

b.  What  would  have  been  the  value  of  h  had  you  used  water  in  the  manometer  ?    Why  then  was  water 
not  used  ? 

c.  What  per  cent  is  your  lung-pressure  of  the  average  lung-pressure  of  the  class  ? 

*  The  mouthpiece  M  consists  of  a  piece  of  glass  tubing  about  3  in.  long  with  the  ends  rounded  in  a  Bunsen  burner. 
Several  of  these  should  be  provided,  and  each  should  be  sterilized  by  being  placed  in  a  beaker  of  boiling  water  for  several 
minutes  after  use  by  a  student. 


50cm. 


25cm. 


FIG.  13 


EXPERIMENT  5  A    (Continued) 

RECORD  OF  EXPERIMENT 
I.  Density  of  mercury 

(a)  Weight  of  bottle  = g. 

Weight  of  bottle  +  mercury  = g. 

Weight  of  bottle  +  water       = g. 

.•.  weight  of  mercury  alone    = g. 

.•.  weight  of  water  aloue         = g. 

.-.  density  of  mercury  = g.  per  cc. 

(6)  From  table  to  A  = cm. 

From  table  to  B  = cm.  .-.  AB  =  cm. 

From  table  to  C  =  cm. 

From  table  to  D  = cm.  .•.  CD  = cm. 

AB-dm=CD.dw,     or     ( ) (dm)  =  ( .)  .  1 

.-.  density  of  mercury  =  g.  per  cc. 

n.  Lung-pressure 

First  level  of  mercury  in  A    =•• cm. 

Second  level  of  mercury  in  A  — cm. 

Difference  =  cm.  .*.  k  = cm. 

p  =  h  '  d  = g.  per  sq.  cm. 

= g.  per  sq.  in. 

= Ib.  per  sq.  in. 

= atmospheres 


[12) 


EXPERIMENT  6 


AKCHIMEDES'  PRINCIPLE  AND  THE  DENSITY  OF  A  SOLID 

I.  To  test  Archimedes'  principle  for  immersed  bodies.    Remove  the  left  pan  from  the  balance  and 
replace  it  by  the  counterpoise  c  (Fig.  14)  which  is  made  as  nearly  as  possible  of  the  same  weight  as 
the  pan.   Adjust  the  balance  by  means  of  the  nut  n  until  the  pointer 

stands  at  the  middle  mark.  Suspend  an  aluminum  cylinder  or  any 
regular  solid  body  of  volume  50  cc.  or  more  from  the  left  arm  of  the 
balance  and  counterpoise  accurately  with  weights  in  the  opposite 
pan.  Record  this  weight. 

Immerse  the  cylinder  in  water,  as  in  Fig.  14.  Carefully  remove 
all  air  bubbles  and  weigh  again.  From  these  observations  find  the 
loss  of  weight  which  the  body  experiences  when  immersed  in  water. 
Measure  the  dimensions  of  the  cylinder  with  the  micrometer  or 
vernier  calipers,  or  simply  by  wrapping  a  fine  silk  thread  about  it,  say 
thirty  times,  and  measuring  the  length  of  the  thread.  Then  compute 
the  volume  in  cubic  centimeters. 

Compare  the  loss  of  weight  obtained  above  with  the  weight  of  the 
liquid  displaced  by  the  body  (that  is,  the  volume  of  the  body  times  the  density  of  the  liquid,  which  is 
in  this  case  1). 

Weigh  the  cylinder  when  it  is  immersed  in  a  beaker  of  gasoline  and  compare  the  loss  of  weight 
with  the  weight  of  the  displaced  liquid,  taking  the  density  of  gasoline  from  the  results  of  Exp.  5,  I. 

State  in  your  notebook  in  your  own  words  the  principle  which  your  experiment  has  shown  to  be  true. 

II.  To  find  the  density  of  a  solid  heavier  than  water  by  the  loss  of  weight  method.   Since  density  is 

defined  as  —     '• — ,  it  is  obvious  that  the  most  direct  way  of  determining  the  density  of  any  regular  solid 
volume 

is  to  find  its  mass  by  a  weighing  and  its  volume  by  direct  measurement.  But  it  would  evidently  be 
quite  impossible  to  find  in  this  way  the  density  of  an  irregular  body,  like  a  lump  of  coal,  because  of  the 
difficulty  of  measuring  its  volume.  The  principle  discovered  in  I,  however,  furnishes  a  very  simple 
way  of  finding  this  volume,  since  it  is  only  necessary  to  find  the  loss  of  weight  which  the  body  ex- 
periences in  water,  in  order  to  find  the  weight  of  an  equal  volume  of  water,  and  this  is  the  same  as 
the  volume  of  the  body,  since  the  density  of  water  is  1.  We  have,  then, 


FIG. 14 


Density  = 


weight  in  air 


loss  of  weight  in  water 

Without  making  any  additional  measurements,  find  the  density  of  the  body  used  in  I,  first,  by  divid- 
ing the  weight  in  air  by  the  volume  as  there  computed  from  its  dimensions,  and  second,  by  dividing 
the  weight  in  air  by  the  volume  of  the  cylinder  as  found  from  the  loss  of  weight  in  water. 

Find  in  the  latter  way  the  density  of  some  irregular  body ;  for  example,  a  brass  weight. 

Questions,  a.  Why  will  an  egg  sink  in  fresh  water  but  float  if  a  considerable  amount  of  salt  is  dissolved 
in  the  water  ?  Try  the  experiment  at  home. 

b.  Using  your  own  weight  in  pounds,  if  you  can  just  float  in  water  with  your  nose  out,  compute  your 
volume  in  cubic  feet. 

c.  In  the  above  experiments  what  became  of  the  weight  "  lost "  ?    If  in  doubt  weigh  a  dish  of  water, 
then  suspend  the  solid  in  it  from  a  tripod,  taking  care  that  the  solid  does  not  touch  the  dish,  and  weigh 
again.    Is  the  second  weight  of  the  dish  more  or  less  than  the  first,  and  how  much  ?  Why  ?    (Note  that  the 
level  of  the  water  is  raised  when  the  solid  is  immersed.) 

[13] 


EXPERIMENT  6    (Continued) 
RECORD  OF  EXPERIMENT 


I.  Archimedes'  principle 

First  Observation 

Diameters cm. 

Length  = 

.-.  volume  = 

Weight  of  cylinder  in  air       = 
Weight  of  cylinder  in  water  = 
Loss  of  weight  in  water 
Weight  of  displaced  water     =• 
Per  cent  of  difference  = 


Second  Observation 

cm. 

cm. 

cc. 

g-    • 

g- 

g- 

g- 


Third  Observation 
...  cm. 


Mean 


Weight  of  cylinder  in  gasoline  = g. 

Loss  of  weight  in  gasoline         = g. 

Weight  of  displaced  gasoline     = g. 

Per  cent  of  difference  =  ... 


II.  Density  of  solid  used  in  I  and  of  an  irregular  solid 

(a)  Density  of  aluminum  =  mass  -4-  volume  from  dimensions       = 

(6)  Density  of  aluminum  =  mass  •*-  volume  from  loss  of  weight  = 

Per  cent  of  difference  =  

Weight  of  brass  body  in  air  =  

Weight  in  water  = 

.•.  density  of  brass  = 

Accepted  value  =  8.4 


[14] 


EXPERIMENT  7 


ARCHIMEDES'  PRINCIPLE  AND  THE  DENSITY  OF  A  LIQUID 

I.  To  test  Archimedes'  principle  for  floating  bodies.  Place  in  a  deep  vessel  of  water  (see  Fig.  9)  a 
piece  of  thin-walled,  cylindrical  glass  tubing  about  |  in.  in  diameter  and  24  in.  long,  loaded  with 
shot  at  the  lower  end  (Fig.  15).  (For  the  sake  of  convenience  in  II  it  is  best  to  load  the  tube 

first  in  a  vessel  of  gasoline  until  it  sinks  to  within,  say,  2  cm.  of  the  top  and  then  to  transfer 
it  without  change  in  the  load  to  the  vessel  of  .water.)  Place  a  rubber  band  about  the  tube 
at  the  exact  point  to  which  it  sinks  in  the  water.  Remove  the  tube  from  the  water,  wipe 
it  dry,  and  then  weigh  it  with  the  contained  shot.  Measure  the  diameter  of  the  tube  in  four 
or  five  different  places  between  the  rubber  band  and  the  bottom,  and  measure  the  distance 
from  the  rubber  band  to  the  bottom.  From  these  two  measurements  compute  the  volume,  and 
therefore  the  weight,  of  the  water  displaced  by  the  floating  body. 

Infer  from  your  results  the  general  law  of  flotation,  and  state  it  in  your  notebook. 

II.  Density  of  a  liquid  by  the  principle  of  flotation,    (a)    Constant-weight  hydrometer.   Im- 
merse the  tube  with  its  contents  in  a  vessel  of  gasoline.    Since  the  tube  will  float  only  when 
the  weight  of  the  displaced  liquid  is  equal  to  the  weight  of  the  floating  body,  and  since  gaso- 
line is  less  dense  than  water,  the  tube  must  sink  to  a  greater  depth  in  the  lighter  liquid  than 
it  did  in  water,  for  example,  to  some  point  C.    Place  a  rubber  band  at  this  point,  and  then 
remove  and  measure  the  length  immersed. 

If  ^  is  the  length  of  the  tube  immersed  in  water  and  ?2  the  length  immersed  in  gasoline,  then 
the  density  of  gasoline  must  be  IJl^  times  the  density  of  water ;  for  if  A  represents  the  area  of  the 
cross  section  of  the  tube,  the  weight  of  the  water  displaced  by  the  tube  is  Al^ ;  and  if  d  is  the     FlG  15 
density  of  gasoline,  the  weight  of  the  displaced  gasoline  is  Al2d ;  and  since  these  weights  are 
equal,  being  both  equal  to  the  weight  of  the  floating  body,  we  have  Alzd  =  Al1;  that  is,  d=ljlf 

Test  your  result  by  means  of  a  commercial  constant-weight  hydrometer  (Fig.  16). 

(5)    Constant-volume  hydrometer.    Drop  shot  into  a  test  tube  which  has  been  drawn  out  to  the 
shape  shown  in  Fig.  17  until,  when  immersed  in  gasoline,  it  sinks  to  the  mark  a  on  the  narrow  part 
of  the  stem.    Remove  the  tube,  dry,  and  weigh  with  the  contained  shot.    Immerse 
in  water,  add  more  shot  until  the  tube  sinks  to  the  same  mark,  remove,  dry,  and 
weigh  again.   The  volume  of  the  liquid  displaced  is  the  same  in  the  two  cases,  and 
the  weight  of  this  volume  is  equal  to  the  weight  of  the  tube  and  its  contents.    The 
specific  gravity,  or  density,  of  the  gasoline  may  therefore  be  found  at  once,  since 
the  data  are  available  for  finding  the  weight  of  a  given  volume  of  gasoline  and  the 
weight  of  an  equal  volume  of  water.  Compare  the  results  with  those  obtained  in  (a). 

State  in  your  notebook  what  two  general  methods  you  have  discovered  for 
finding  the  densities  of  liquids. 

Questions,    a.  Can  you  see  any  reason  why  a  constant-weight  hydrometer  made 
with  a  narrow  stem  (Fig.  16)  is  a  much  more  accurate  instrument  for  determining 
the  densities  of  liquids  than  a  cylindrical  constant-weight  hydrometer  like  that  shown      FIG.  16       FIG.  17 
in  Fig.  15  ? 

b.  If  any  convenient  solid  is  weighed  first  in  air,  then  in  water,  and  then  in  some  other  liquid,  for 
example,  gasoline,  the  three  weighings  will  furnish  data  for  determining  the  density  of  gasoline.    Write 
an  explanation  of  this  in  your  notebook,  and  compute  the  density  of  gasoline  from  the  weighings  of  this 
sort  which  you  made  in  Exp.  6. 

c.  If  a  tube,  like  that  used  in  I,  sank  36  cm.  in  water  and  20  cm.  in  sulphuric  acid,  what  was  the  density 
of  the  acid  ?    How  far  would  the  same  tube  sink  in  a  salt  solution  of  density  1.125  ? 

[15] 


EXPERIMENT  7    (Continued) 

RECORD  OF  EXPERIMENT 
I.  Archimedes'  principle  for  floating  bodies 

First  diameter     = cm.  Length  immersed  = cm. 

Second  diameter  = cm.  Area  of  cross  section  = sq.  cm. 

Third  diameter    = cm.  Weight  of  displaced  water  =  g. 

Fourth  diameter  = cm.  Weight  of  tube  and  shot     = g. 

Mean  diameter     = cm.  Per  cent  of  difference  = 

.  (a)  Constant-weight  hydrometer  (&)  Constant-volume  hydrometer 

Length  in  water  =  cm.  Weight  in  water  = g. 

Length  in  gasoline  = cm.  Weight  in  gasoline  = g. 

.-.  density  of  gasoline  =  .-.  density  of  gasoline  — 

By  commercial  hydrometer  = ,  Difference  between  (a)  and  (&)  = % 


[16] 


EXPERIMENT  8 


FIG.  18 


I.  By  weighing  first  in  air  and  then  when  immersed  in  water  with  the  aid  of  a  sinker.    If  a  body 
is  lighter  than  water,  the  weight  of  an  equal  volume  of  water  may  be  obtained  with  the  aid  of  a  sinker. 

Use  a  wooden  block  B  (Fig.  18)  which  has  been  paraffined  so  as  to  prevent  the 

absorption  of  water.   Weigh  the  block  alone  in  air  and  then  with  the  sinker 

attached,  the  block  being  in  air  and  the  sinker  S  in  water,  as  shown  in  the 
figure.  Lastly,  weigh  when  the  block  and  the  sinker  are  both  under  water. 
The  difference  between  the  second  and  the  third  weighings  is  evidently  the 
buoyant  effect  of  the  water  on  the  block  alone,  that  is,  it  is  the  weight  of  the 
water  displaced  by  the  block,  and  hence  it  is  also  the  volume  of  the  block. 
From  this  difference  and  the  weight  of  the  block  in  air  obtain  the  density  of 
the  block  of  wood  used  in  this  experiment. 

Explain  in  your  notebook  how  you  calculated  the  density  of  wood,  and  why 
your  method  of  procedure  gives  this  density. 

II.  From  the  weight,  length,  breadth,  and  height  of  a  block.    Measure  the 
three  dimensions  of  the  block  with  a  meter  stick  held  on  edge,  as  in  Fig.  2. 
From  these  measurements  and  the  weight  of  the  block,  obtained  in  I,  compute 
the  density  of  the  wood. 

III.  From  the  depth  to  which  a  block  sinks  in  water.    Wax  a  pin  to  the 

end  of  a  metric  rule  ab,  arranged  as  in  Fig.  19,  and  take  the  reading  of  the  point  on  this  rule  at 
which  it  meets  the  straightedge  CD  when  the  pin  point  just  touches  the  corner  m  of  the  floating 
block.    Then  take  the  reading  on  ab  when  the  pin  point  just  touches  the  surface  of  the  water,  say, 
1  cm.  away  from  the  edge  of  the  block.    The  difference  between  these 
two  readings  subtracted  from  the  height  of  the  block  would  give  the 
distance  which  the  block  sinks  in  the  liquid  if  the  surface  of  the  block 
were  accurately  horizontal.    In  order  to  obtain  as  accurate  a  value  as 
possible  for  this  distance,  repeat  the  measurements  at  each  corner  of  the 
block,  and  take  a  mean  of  these  four  differences.   From  this  mean  differ- 
ence find  the  distance  h'  which  the  block  sinks  in  water.    Then,  from  h' 
and  the  height  h  of  the  block  compute  its  density  d  from  the  relation 


»  FIG.  19 

Questions,    a.  Prove  in  vour  notebook  that  the  above  equation  for  the  density  of  the  block,  namely, 

h' 
d=s  —  )  follows  at  once  from  the  statement  of  Archimedes'  principle  as  applied  to  floating  bodies  ;  namely, 

"  The  weight  of  the  floating  body  is  equal  to  the  weight  of  the  liquid  which  it  displaces."  (Eemember  that 
weight  =  volume  x  density ;  so  that,  if  A  represents  the  area,  of  the  top  of  the  block,  the  weight  of  the  block 
is  Ahd,  while  the  weight  of  the  displaced  liquid  is  Ah'd',  d'  in  this  case  being  1.) 

&.  Can  you  see  from  your  analysis  any  general  relation  which  must  always  exist  between  the  density  of 
a  body  floating  on  water,  the  volume  of  the  body,  and  the  volume  which  is  beneath  the  surface  ? 

c.  How  much  deeper  will  a  10  cm.  cube  of  oak  sink  in  water  than  a  cube  of  pine  of  like  dimensions,  if 
the  density  of  oak  is  .8  and  that  of  pine  .5  ? 

d.  Why  are  life  preservers  filled  with  cork  instead  of  with  pine  ? 

e.  Why  is  it  unnecessary  to  know  the  density  of  the  sinker  S  in  this  experiment  ? 

[171 


EXPERIMENT  8    (Continued) 

RECORD  OF  EXPERIMENT 

I.  Density  by  Archimedes'  principle  for  a  solid  lighter  than  water 

Weight  of  block  alone  in  air  =  g. 

Weight  when  block  is  in  air  and  sinker  in  water  = g. 

Weight  when  both  block  and  sinker  are  in  water  = g. 

.-.  density  of  wood  =  

II.  From  the  weight,  length,  breadth,  and  height  of  the  block 

Length  of  block  = cm.  .-.volume  =  cc. 

Breadth  of  block  = cm.  .-.  density  =  

Height  of  block    = cm.  %  of  difference  in  I  and  II  = 

III.  From  the  depth  to  which  the  block  sinks  in  water 

First  Corner                 Second  Corner                Third  Corner                Fourth  Corner 
Reading  with  pin  touching  water  = cm cm.  cm.   , cm. 

Reading  with  pin  touching  block  = cm.  cm cm cm. 

Differences  = cm cm cm.  cm. 

Mean  difference  = ,   h  = ,    .-.  h'  =  •.  d  = 


[18] 


EXPERIMENT  9 


FIG.  20 


THE  RELATION  BETWEEN  THE  PRESSURE  AND  THE  VOLUME  OF  A  GIVEN  MASS 
OF  GAS  AT  CONSTANT  TEMPERATURE 

I.  Verification  of  Boyle's  law.    The  quantity  of  air  whose  pressure  and  volume  are  to  be  varied  is 
confined  by  the  thread  of  mercury  AB  in  one  end  BC  (Fig.  20)  of  a  glass  tube  about  1  m.  long  and 
of  uniform  bore  1  mm.  in  diameter.    Since  the  cross  section  of  the  tube  is  uniform,  the  volume  of  the 
confined  air  is  proportional  to  the  length  of  BC. 

With  the  tube  vertical,  closed  end  C  down,  the  pressure  on  the  confined  air  is  atmospheric  pres- 
sure plus  the  pressure  due  to  the  thread  of  mercury.  Both  of  these  pressures  are  in  centimeters  of 
mercury  and  therefore  may  be  added. 

(a)  Read  the  barometer  in  centi- 
meters. 

Measure  AB  in  centimeters  and  add 
to  the  barometer  reading  for  the  first 
pressure  Pr 

Measure  BC  in  centimeters  and  call 
this  length  the  first  volume  V . 

(6)  Rotate  the  tube  approximately  45°.  Now  the  pressure  due  to  the  thread  of  mercury  AB  is  the 
vertical  height  of  AB. 

Measure  the  height  of  A,  and  of  B,  above  the  table  and  take  the  difference  to  get  the  vertical  height 
of  AB.  Add  this  difference  to  the  barometer  reading  to  obtain  P2.  Measure  BC,  as  before,  to  get  F2. 

(c)  In  the  third,  or  horizontal,  position  the  mercury  thread  neither  increases  nor  decreases  the 
pressure  on  the  confined  air,  which  is,  therefore,  at  atmospheric  pressure.  Measure  BC  to  get  Fg. 

(<f)  Rotate  the  tube  approximately  45°,  closed  end  C  up.  The  vertical  height  of  AB  must  now 
be  subtracted  from  the  barometer  reading  to  obtain  P4.  Why  ?  Measure  BC  to  get  F4. 

(e)  Take  measurements  with  the  tube  vertical,  closed  end  up. 

II.  Algebraic  statement  of  an  inverse  proportion  ;  for  example,  Boyle's  law.   (a)  Note  that  the  differ- 
ence between  any  P  Fand  the  mean  PFis  seldom  more  than  2% .   Then  we  may  infer,  barring  errors,  that 

P1  Vl  =  P2  F2  =  Pg  Fg,  etc.,  or,  more  simply,  P  F  =  constant. 

Thus  we  see  that  as  P  decreases,  F  must  increase  if  the  product  remains  constant,  that  is,  P  is 
inversely  proportional  to  F,  and  the  equation  PV=  constant  represents  an  inverse  proportion. 
(6)  What  relation  do  you  note  from  your  data  between  Vj  Vl  and  PjPz,  etc.  ? 
This  is  another  way  of  stating  an  inverse  proportion. 

III.  Graphical  representation  of  an  inverse  proportion,    (a)  Using  the  equation  P  F  =  constant, 
where  this  constant  is  the  mean  PF,  compute  the  pressures  which  would  correspond  to  two,  three, 
and  four  times  the  greatest  measured  volume. 

(5)  Compute  the  volumes  which  would  correspond  to  two,  three,  and  four  times  the  greatest 
observed  pressure. 

(c)  Plot  these  six  pressures  and  the  corresponding  volumes,  together  with  the  five  pressures  and 
volumes  you  obtained  experimentally,  representing  pressures  as  horizontal  distances  and  volumes  as 
vertical  distances.  The  smooth  curve  drawn  through  these  points  is  called  a  hyperbola. 

Questions,  a.  What  relation  exists  between  the  pressure  and  the  volume  of  a  mass  of  gas  at  the  constant 
temperature  ? 

b.  Give  two  equations  showing  this  relationship. 

c.  What  is  the  name  of  a  curve  which  represents  an  inverse  proportion  ? 

[19] 


EXPERIMENT  9    (Continued) 
RECORD  OF  EXPERIMENT 


POSITION  OF 
TUBE 

VOLUME  OF 
CONFINED 
AIK  (DC) 

HEIGHT  OF  A 
ABOVE  TABLE 

HEIGHT  OF  B 
ABOVE  TABLE 

DIFFERENCE 
(VERTICAL 
HEIGHT 
OF  AD) 

BAROMETER 
READING 

PRESSURE 

PRESSURE 

TIMES 

VOLUME 

DIFFERENCE 
FROM  MEAN 
PV 

(a) 

<&) 

(«) 

(d) 

(«) 

Compute  the  ratios  below,  giving  three  significant  figures.  Mean  PV  —  ........................  =  constant. 


Difference  =  ...  .    Difference  =  ...  .    Difference  =  ...  .    Difference  = 


[20] 


EXPERIMENT  9  A 

TO  FIND  THE  WEIGHT  OF  AIR  IX  ONE  CUBIC  CENTIMETER,  IN  ONE  LITER,  IN  ONE 
CUBIC  METER,  AND  IN  THE  LABORATORY* 

(a)  Attach  a  piece  of  rubber  tubing  and  a  pinchcock  to  a  bottle  f  of  about  2-liter  capacity. 
reigh  the  bottle  and  attachments  to  hundredths  of  a  gram. 

(6)  With  an  air  pump  exhaust  as  much  of  the  air  from  the  bottle  as  you  can  by  pumping 
moderately  for  two  or  three  minutes,  close  the  pinchcock  tightly,  and  again  weigh. 

(c)  Place  the  bottle  and  tubing  neck  end  down  in  a  large  vessel  of  water  at  room  temperature, 
open  the  pinchcock,  and  let  the  water  in  to  take  the  place  of  the  exhausted  ah*.   Push  the  bottle  down 
into  the  vessel  of  water  until  the  water  in  the  bottle  is  just  level  with  the  water  outside  and  then 
close  the  pinchcock.    Remove  the  bottle,  wipe  off  the  water,  and  weigh  the  bottle,   attachments, 
and  water. 

(d)  Measure  the  length,  width,  and  height  of  the  laboratory  in  meters.    Compute  the  quantities 
indicated  in  the  record  of  the  experiment. 

(e)  Take  the  temperature  of  the  room  and  the  barometer  reading  for  the  sake  of  the  use  they 
will  be  in  answering  some  of  the  questions. 

Questions,  a.  In  (c)  just  before  closing  the  pinchcock  what  was  the  pressure  of  the  air  remaining  in 
the  bottle  in  centimeters  of  mercury  ? 

&.  From  the  weight  of  1  cc.  of  air  which  you  obtained  and  the  barometer  reading,  with  the  aid  of  Boyle's 
law  compute  the  weight  of  1  cc.  at  76  cm.  pressure,  at  the  temperature  of  the  laboratory. 

c.  The  density  of  air  at  76  cm.  pressure,  containing  some  moisture,  is  about  .00122  at  15°  C.  or  59°  F., 
.00120  at  20°  C.  or  68°  F.,  .00118  at  25°  C.  or  77°  F.,  and  .00116  at  30°  C.  or  86°  F.    From  these  values  find 
by  interpolation  the  density  of  air  at  76  cm.  pressure,  at  the  temperature  of  the  laboratory.    By  what  per 
cent  does  your  value  in  c  differ  from  this  value  ? 

d.  About  how  deep  would  mercury  have  to  be  if  it  covered  the  whole  of  the  earth  to  a  uniform  depth  to 
have  the  same  weight  as  all  the  air  surrounding  the  earth  ? 


(a)  Weight  of  bottle  = g. "] 


RECORD  OF  EXPERIMENT 

weight  of  air  exhausted  = g. 


(6)  Weight  of  bottle  (exhausted)  = g.  J 

C  .-.  volume  of  air  exhausted  (c-b)  ~] 

(c)  Weight  of  bottle  aiid  water      = g.    -(  >  = ...cc 

L       at  atmospheric  pressure  J 

(c?)  Length  of  laboratory  = m.,    width  = m.,    height  = in. 

.-.  volume  =  cu.  m. 

(e)  Temperature  of  room  = °C.,    or °F.,    barometer  reading  = cm. 

Weight  of  1  cc.  of  air  (density)  =  ,         weight  of  1  liter  of  air  = g. 

Weight  of  1  cu.  m.  of  air  = kg. 

Weight  of  air  in  laboratory  =  kg.  = Ib. 

From  question  b  density  = g.  per  cc. 


Per  cent  of  difference  = 
From  question  c  density  =  g.  per  cc. 

*  On  account  of  the  very  considerable  work  involved  in  preparing  a  large  number  of  air-tight  bottles  for  this  experiment 
and  drying  them  after  use  before  they  are  in  readiness  for  another  section,  unless  an  ample  number  of  spheres  with  good 
stopcocks  are  available,  the  authors  would  suggest  that  this  experiment  be  performed  but  once,  by  the  teacher  and  class 
together,  rather  than  by  each  pupil. 

t  A  hollow  metal  sphere  with  stopcock  may  be  used  without  the  tubing.  All  joints  in  either  case  should  be  made  air- 
tight with  vaseline,  and  the  volume  of  the  bottle  or  sphere  should  have  been  previously  determined  and  marked  upon  it. 

[21] 


EXPERIMENT  10 
THE  MOLECULAR  CONSTITUTION  OF  MATTER 

(a)  Fill  a  long,  narrow  test  tube  or,  better,  the  hydrometer  tube  of  Fig.  15  about  half  full  of  water. 

(5)  Then,  to  prevent  mixing,  incline  the  tube  as  much  as  possible  while  you  carefully  pour  in 
alcohol  till  the  tube  is  filled.  If  the  alcohol  has  been  poured  into  the  tube  with  sufficient  care,  you 
should  be  able  to  observe  a  distinct  surface  of  demarcation  separating  the  two  liquids. 

(<?)  Place  the  thumb  tightly  over  the  top  of  the  tube  and  slowly  invert,  and  at  the  same  time 
observe  carefully  what  takes  place. 

(c?)  Keeping  the  thumb  pressed  tightly  against  the  end  of  the  tube,  invert  and  restore  it  to  its 
original  position  several  times,  until  the  liquids  are  thoroughly  mixed.  During  this  inverting  process 
has  your  thumb  been  drawn  into  or  pressed  into  the  tube  ? 

Questions,  a.  Will  the  combined  volume  of  given  volumes  of  water  and  alcohol  be  the  sum  of  the 
separate  volumes  ? 

b.  Will  a  bushel  basket  full  of  baseballs  and  a  bushel  basket  full  of  small  marbles  fill  two  bushel  baskets 
when  thoroughly  mixed  ? 

c.  How  do  you  account  for  the  combined  volume  of  the  alcohol  and  water  being  less  after  they  are  mixed  ? 


[23] 


EXPERIMENT  10  A 


COOLING  BY  EVAPORATION;    SATURATION;   DEW  POINT 
FREEZING  BY  EVAPORATION 

I.  Cooling  by  evaporation.    Let  three  4-oz.  bottles,  the  first  half-full  of  ether,  the  second  half-full 
of  alcohol,  and  the  third  half-full  of  water,  be  provided.    The  bottles  should  be  closed  with  small 
corks  and  should  have  been  standing  in  the  room  long  enough  to  acquire  room  temperature. 

(a)  Swing  a  thermometer  in  the  air  for  a  minute  and  then  record  the  temperature  of  the  room. 
(£)  Insert  the  thermometer  in  the  ether  bottle,  and  at  the  end  of  half  a  minute  record  the  temper- 
ature of  the  ether.    Take  the  reading  while  the  bulb  is  in  the  liquid.    In  the  same  way  take  the 
temperature  of  the  alcohol  and  of  the  water. 

(c)  From  the  bottles  pour  enough  of  each  liquid  into  the  evaporating  dishes  of  Fig.  21  to  cover  the 
bulbs  of  the  thermometers  and  about  the  same  amount  of  ether  into  a  test  tube  supported  in  a 
beaker  or  test-tube  rack.  Watch  the  thermometers 
ten  or  fifteen  minutes  and  record  the  temperature 
of  each.  (Pins  driven  into  a  4  x  4-in.  block  will 
prevent  sliding  and  breaking  of  thermometers  and 
make  a  convenient  support.) 

(<T)  Put  a  drop  of  ether,  of  alcohol,  and  of 
water  upon  the  hand  and  note  the  order  of  dis- 
appearance and  also  the  order  of  the  cooling  sen- 
sations which  they  produce. 

State  in  your  notebook  what  effect  your  experi-  FIG.  21 

lents  have  shown  evaporation  to  have  upon  the 

smperature  of  the  evaporating  body.   Explain,  if  you  can,  why  the  temperature  of  the  ether  in  the  test 
ibe  was  different  from  that  in  the  evaporating  dish.   Explain  with  the  aid  of  this  experiment  and  the 
swer  to  the  first  question  why  the  ether  in  the  evaporating  dish  had  a  lower  temperature  than  the 
3ohol,  and  the  alcohol  a  lower  temperature  than  the  water. 

When  a  body  is  below  room  temperature  it  is  continually  receiving  heat  from  the  room.    When 
liquids  in  the  evaporating  dishes  had  reached  a  constant  temperature,  what  relation  existed  be- 
reen  the  amount  of  heat  which  they  lost  per  second  by  evaporation  and  the  amount  which  they 
reived  per  second  from  the  room  ? 

II.  Saturation.    A  space  in  which  evaporation  will  no  longer  take  place  from  the  surface  of  a 
given  liquid  placed  within  the  space  is  said  to  be  saturated  with  the  vapor  of  the  liquid.    This  means 
simply  that  the  space  already  contains  as  much  of  the  vapor  of  the  liquid  as  it  is  capable  of  holding 
at  the  given  temperature. 

(a)  Cover  the  bulb  of  the  thermometer  with  a  bit  of  absorbent  cotton,  dip  it  into  the  bottle  of  ether, 
and  then  lift  it  so  that  the  bulb  and  cotton  are  above  the  surface  of  the  ether  but  still  in  the  bottle. 
Watch  the  temperature  for  a  minute  or  two  and  then  record.  Transfer  the  covered  bulb  from  the  bottle 
to  the  test  tube  and  hold  it  there  above  the  surface.  After  a  minute  or  two  record  the  temperature. 
Lift  the  covered  bulb  out  into  the  air  and  record  the  temperature  after  it  has  become  constant.  What 
do  you  learn  from  this  experiment  regarding  the  temperature  which  a  thermometer  surrounded  with 
a  cloth  soaked  in  a  liquid  will  maintain  in  a  space  which  is  saturated  with  a  vapor  of  the  liquid  ?  in 
a  space  which  is  partially  saturated  ?  in  a  space  which  is  free  from  this  vapor,  that  is,  which  is  dry  ? 

(6)  Wrap  some  fresh  cotton  about  the  bulb  of  the  thermometer,  and  dip  it  into  the  bottle  of 
water:  then  remove  the  thermometer  and  swing  it  in  the  room  until  its  reading  becomes  constant 

[25] 


EXPERIMENT  10  A  (Continued) 


Would  this  reading  be  any  different  if  there  were  no  water  vapor  already  in  the  room?  What  would 
it  be  if  the  air  were  already  saturated  with  water  vapor  ?  Can  you  see,  then,  how  the  difference 
between  the  readings  of  a  thermometer  whose  bulb  is  kept  dry  and  one  whose  bulb  is  kept  moist 
gives  us  some  information  regarding  the  dryness  of  the  atmosphere  ? 

III.  Dew  point.    The  amount  of  vapor  which  a  given  space  can  hold  is  found  to  decrease  rapidly 
as  the  temperature  decreases.    Hence,  if  we  lower  the  temperature  of  a  space  which  is  already  satu- 
rated with  any  vapor,  a  part  of  it  condenses.    If  we  lower  the  temperature  of  a  space  which  is  not 
saturated,  but  which  contains  some  vapor,  nothing  happens  until  the 
temperature  is  reached  at  which  the  amount  of  vapor  which  already  exists 
in  the  space  is  the  amount  which  saturates  it.   Then  condensation  begins. 
The  temperature  at  which  water  vapor  begins  to  condense  out  of  the  atmosphere 
as  the  temperature  is  lowered,  is  called  the  dew  point.    It  varies,  of  course, 
from  day  to  day,  depending  upon  the  amount  of  water  vapor  in  the 
atmosphere. 

(a)  Fill  the  polished  metal  tube  *  of  Fig.  22  two-thirds  full  of  ether, 
and  force  air  very  gently  through  it  by  squeezing  the  bulb.  This  process 
facilitates  cooling,  since  it  increases  enormously  the  evaporating  surface, 
every  bubble  having  a  large  surface  through  which  evaporation  can  take 
place.  The  temperature  existing  within  the  tube  when  the  first  cloudiness 

begins  to  appear  upon  the  polished  surface  is  the  dew  point,  for  it  is  the  temperature  at  which  the 
layers  of  air  in  contact  with  the  tube  become  saturated  and  begin  to  deposit  their  moisture.  As  soon 
as  this  cloudiness  is  noticed,  take  the  reading  of  the  thermometer,  and  then  stop  the  current  and  notice 
the  temperature  at  which  the  cloudiness  disappears.  Take  pains  in  these  experiments  not  to  breathe 
upon  the  polished  surface.  Repeat  the  whole  operation  until  the  temperatures  of  appearance  and  disap- 
pearance do  not  differ  by  more  than  1°.  Take  the  mean  of  the  two  temperatures  as  the  dew  point. 


FIG.  22 


re. 

P 

t°C. 

P 

t°C. 

P 

t°C. 

P 

t°C. 

P 

-  10° 

2.2 

-  1° 

4.2 

8° 

8.0 

17° 

14.4 

26° 

25.0 

-    9° 

2.3 

0° 

4.6 

9° 

8.5 

18° 

16.3 

27° 

26.5 

-    8° 

2.6 

1° 

4.9 

10° 

9.1 

19° 

16.3 

28° 

28.1 

-    7° 

2.7 

2° 

5.3 

11° 

9.8 

20° 

17.4 

29° 

29.7 

-    6° 

2.9 

3° 

5.7 

12° 

10.4 

21° 

18.5 

30° 

31.5 

-    6° 

3.2 

4° 

6.1 

13° 

11.1 

22° 

19.6 

35° 

41.8 

-    4° 

3.4 

6° 

6.5 

14° 

11.9 

23° 

20.9 

40° 

54.9 

-    3° 

3.7 

6° 

7.0 

15° 

12.7 

24° 

22.2 

46° 

71.4 

2° 

3.9 

7° 

7.5 

16° 

13.6 

25° 

23.5 

(5)  From  the  dew  point  and  the  accompanying  table  find  the  humidity  of  the  atmosphere.  This  is 
the  ratio  between  the  amount  of  moisture  in  the  atmosphere  at  the  time  of  the  experiment  and  the 
total  amount  which  it  is  capable  of  holding  at  the  temperature  of  the  room.  It  is  found  by  dividing 
the  pressure  of  saturated  water  vapor  at  the  temperature  of  the  dew  point  by  the  pressure  of  saturated 
water  vapor  at  the  temperature  of  the  room  (see  table),  t 

IV.  Freezing  by  evaporation.  Place  a  few  drops  of  water  upon  the  table  and  set  the  polished  metal 
tube  containing  ether  upon  it.  Force  air  through  the  ether  rapidly  and  see  if  you  can  freeze  the  tube 
to  the  table. 

*  This  experiment  can  be  performed  almost  as  successfully  by  dropping  bits  of  ice  slowly  into  -water  contained  in  a 
polished  vessel,  and  noting  the  temperature  at  which,  with  continual  stirring,  the  cloud  appears  on  the  outside.  If  the  dew 
point  is  below  zero,  salt  should  be  added,  bit  by  bit,  to  the  iced  water  until  the  cloud  appears. 

t  The  table  shows  the  pressure  P,  in  millimeters  of  mercury,  of  water  vapor  saturated  at  temperature  t°G. 

[26.1 


EXPERIMENT  10  A  (Continued) 


Questions,    a.  What  effect  does  evaporation  have  on  the  temperature  of  a  liquid  ? 

b.  In  I,  (c),  why  does  not  the  temperature  of  the  ether  in  the  test  tube  fall  as  low  as  in  the  evaporating  dish? 

c.  From  the  data  of  I,  (a)  and  I,  (&)  decide  whether  evaporation  is  taking  place  at  the  surface  of  a  liquid 
in  a  closed  bottle. 

d.  See  that  all  questions  at  end  of  I,  II,  and  III  are  answered. 

RECORD  OF  EXPERIMENT 


ETHER 

ALCOHOL 

WATER 

I.  (a)  Temperature  of  room  =                         ..  °C. 

(ft)  Temperature  of  liquid  in  bottle 

(c)  Temperature  of  liquid  in  evaporating  dish 

Temperature  of  ether  in  test  tube 

(d)  Order  of  disappearance 

Order  of  cooling  sensation  produced 

II.  (a)  Temperature  of  cotton-covered  bulb 

In  ether  bottle  = °C. 

Above  ether  in  bottle       = °C. 

Above  ether  in  test  tube  = °C. 

In  still  air  = °C. 

(6)  Temperature  of  cotton-covered  bulb,  wet  with  water  and  swung  = °C. 

HE.  (a)  Cloudiness  appears  at °  C.,  disappears  at °C.  .-.  dew  point  =  . 

(ft)  Pressure  of  saturated  vapor  at  dew  point  =  mm.  of  mercury. 

Pressure  of  saturated  vapor  at  room  temperature  = mm.  of  mercury. 

.-.  relative  humidity  = %. 


'C. 


[27] 


EXPERIMENT  11 


FIG.  23  A 


RESULTANT  OF  TWO  FORCES 

I.  Parallel  forces.   Support  two  spring  balances*  from  nails,  pegs,  or  tripod  rods,  as  in  Fig.  23  A, 
and  so  choose  the  distance  between  the  supports  that  the  meter  stick  ab  is  supported  at,  say,  the 
10-cm.  and  90-cm.  divisions. 

Record  the  readings  of  the  bal- 
ances 1  and  2  when  they  support  the 
meter  stick  without  the  weight  W. 

Hang  from  the  50-cm.  mark  a 
mass  W  which  you  have  already 
weighed  on  one  of  the  spring  bal- 
ances, and  which  is  large  enough 
to  stretch  it  nearly  to  its  limit. 

Read  the  balances  1  and  2,  and 
call  the  differences  between  these 
readings  and  the  initial  readings 
Fl  and  Fz  respectively. 

Then  take  readings  with  W  placed  successively  at  the  40-cm.,  the  30-cm.,  and  the  20-cm.  mark. 

Let  ?x  and  12  represent  in  each  case  the  distance  in  centimeters  from  the  point  from  which  W  is 
hung  to  1  and  2  respectively. 

Since  the  forces  F^  F^  and  W  are  in  equilibrium,  W  is  said  to  be  the  equilibrant  of  F1  and 

What  single  force  would  replace  Fl  and 
and  produce  the  same  effect;  that  is,  support 
This  force  is  called  the  resultant  of  F1  and  FZ. 

State  in  your  notebook  what  you  learn  from 
rour  results  regarding,  first,  the  magnitude  of  the 

jsultant  of  two  parallel  forces ;  second,  the  product  of  either  of  two  parallel  forces  by  its  distance 
from  the  resultant ;  third,  the  relation  between  the  direction  of  the  resultant  of  Fl  and  FZ,  and  of  W. 

II.  Concurrent  forces.    Fasten  three  spring  balances  to  a  small  ring 
by  strings  about  8  in.  long  and  slip  the  rings  of  the  balances  over 

wooden  pegs  or  nails  in  a  board  AB  about  3  ft.  square  (Fig.  24).   Choose 
such  holes  for  the  pegs  that  each  balance  is  stretched  to  at  least  one 
ilf  of  its  full  range. 

Slip  a  page  of  your  notebook  beneath  the  central  ring,  fasten  it  down 
rith  thumb  tacks  or  weights,  and  with  a  sharp-pointed  pencil  make  a 
lot  on  the  paper  just  at  the  center  of  the  ring.  Displace  the  ring  and 
see  that  its  center  comes  back  exactly  to  the  same  position  as  at  first. 
If  this  is  not  the  case,  the  cause  probably  lies  in  the  friction  which 
exists  between  the  balances  and  the  board,  a  difficulty  which  may  be 
remedied  by  raising  the  rings  slightly  on  the  pegs. 

Make  a  dot  exactly   beneath   each   string  and  as  far  from   a  as 
possible ;  then  take  the  three  balance  readings. 

Unhook  each  balance  from  its  peg  and  note  the  reading  of  the  pointer  as  the  balance  lies  flat  on 
the  table.  If  this  reading  is  less  than  zero,  add  the  suitable  correction  to  the  balance  reading  recorded 
on  the  paper;  if  it  is  more  than  zero,  subtract  the  appropriate  amount. 

*  If  spring  balances  are  not  available,  the  apparatus  may  be  arranged  as  in  Fig.  23  B. 

[29] 


FIG.  23  B 


FIG.  24 


EXPERIMENT  II    (Continued) 


FIG.  25 


Remove  the  paper  and  with  great  care  draw  a  fine  line  from  the  central  point  through  each  of  the 
three  outside  points.  The  direction  of  each  line  will  represent  the  direction  of  the  corresponding  force. 

Measure  off  a  distance  on  each  line  which  shall  be  proportional  to  ^ 

the  corresponding  force,  choosing  any  convenient  scale ;  for  example,  if 
the  forces  are  700,  1000,  and  1200  g.,  they  may  be  conveniently  repre- 
sented by  lines  7,  10,  and  12  cm.  long. 

With  any  two  of  these  lines  as  sides  complete  a  parallelogram,  using 
a  ruler  and  compasses  to  get  the  sides  exactly  parallel.  Draw  the  diag- 
onal of  this  parallelogram  from  the  central  point  a,  measure  its  length, 
and  find  the  magnitude  of  the  force  which  it  represents.  Thus,  if  the 
diagonal  has  a  length  of  134  mm.,  it  would  represent  in  the  foregoing 
illustration  a  force  of  1340  g.  Compare  with  the  reading  of  the  third 
balance. 

State  in  your  notebook  what  you  have  proved  to  be  true  regarding  both  the  magnitude  and  the 
direction  of  the  resultant  of  two  forces  which  meet  at  an  angle. 

Questions,  a.  If  one  singletree  is  attached  20  in.  and  the  other  25  in.  from  the  center-pin  of  a  doubletree 
and  the  combined  pull  of  the  two  horses  is  a  force  of  450  lb.,  with  how  many  pounds  of  force  is  each  horse 
pulling  ? 

b.  If  a  weight  (Fig.  25)  of  50  lb.  is  hung  over  the  middle,  C,  of  a  wire  AB  whose  breaking  strength  is 
50  lb.  and  the  tension  at  B  is  increased,  show  that  the  wire  will  break  when  the  angle  A  CB  becomes  greater 
than  120°. 

RECORD  OF  EXPERIMENT 
I.  Parallel  forces 

Initial  reading  of  balance  1  = g.,  of  balance  2  =  g. 

Weight  W  hung  on  meter  stick  = g. 


BALANCE  1 

BALANCE  2 

PI 

r, 

PI  +  P* 

*ix*i 

^xi, 

W  at  50  cm. 

W  at  40  cm. 

W  at  30  cm. 

W  at  20  cm. 

II.  Concurrent  forces 

Reading  of  balance  1  = 
Reading  of  balance  2  = 
Reading  of  balance  3  = 
Scale  used  1  cm.  = 

Length  of  line  1 
Length  of  diagonal      = 


Correction  = 
Correction  = 
Correction  = 

of  line  2  = 
.-.  resultant  = 


F      = 

•*•     Q 


.-.  error  =  %. 


[30] 


EXPERIMENT  12 

THE  LAWS  OF  THE  PENDULUM     ' 

I.  To  find  whether  or  not  the  time  of  swing  is  different  for  different  amplitudes  and  different 
weights,    (a)  Attach  with  sealing  wax   a  small  weight  —  preferably,  a  steel  ball   about  ^  in.  in 
diameter  —  to  a  fine  thread  about   180  cm.  long,  and  suspend  it  in  a  wooden  clamp  with  square 
jaws,  like  that  shown  in  Fig.  26. 

Let  a  student,  A,  set  his  eye  in  some  particular  position,  such  that  the  thread  is  in 
line  with  some  fixed  mark  or  small  object.  Then  let  the  pendulum  be  set  into  vibration 
through  an  arc  10  or  12  cm.  long.  Let  a  second  student,  B,  keep  his  eye*  on  the 
second  hand  of  a  watch  while  A  taps  with  his  pencil  upon  the  table  at  the  instant 
of  each  passage  of  the  pendulum  past  the  fixed  mark.  When  B  is  ready  let  him  call 
"  now"  at  the  instant  of  some  tap,  and  record  the  hour,  minute,  and  second  at  which  he 
called  it ;  let  A  take  up  the  count  "  one  "  at  the  instant  of  the  next  tap  and  continue 
up  to  one  hundred.  Let  B  record  again  the  hour,  minute,  second,  and,  if  possible,  the 
fraction  of  a  second,  at  which  the  count  "  one  hundred  "  occurs. 

Increase  the  amplitude  of  swing  to  about  30  cm.  and  again  observe  the  time  of  one 
hundred  vibrations  exactly  as  before.  Make  another  trial  when  the  amplitude  has  been 
increased  to  2  m.  or  more. 

(5)  Suspend  another  pendulum,  which  is  of  the  same  length  from  the  support  to 
the  center  of  the  bob  but  of  quite  different  mass  and  material  (for  example,  use  for  the  bob  a  lead 
bullet),  and  see  whether  one  pendulum  gains  at  all  upon  the  other  when  they  are  set  going  together 
through  an  arc  of  30  or  40  cm. 

So  long  as  the  amplitude  of  swing  is  small,  do  you  find  that  the  period  depends  upon  it  at  all  ? 
What  is  the  effect  of  a  very  large  amplitude  ?  What  influence  has  the  weight  of  the  bob  upon  the 
period  of  a  pendulum  ? 

II.  To  find  the  relation  between  the  lengths  of  two  pendulums  and  their  periods.    Replace  the  last 
pendulum  by  a  second  one,  which  has  a  bob  like  the  first,  and  adjust  its  length  by  slipping  it  through 
the  clamp,  the  screw  being  only  moderately  tight,  until  it  is  just  one  fourth  as  long  as  the  first  pen 
dulum.    (The  length  of  each  is  the  distance  from  the  bottom  of  the  clamp  to  the  top  of  the  ball  plus 
the  radius  of  the  ball.) 

Using  a  small  amplitude,  take  the  time  of  100  vibrations. 

Make  the  pendulum  one  ninth  of  its  original  length  and  take  the  time  of  100  vibrations. 

With  the  aid  of  the  ratios  found,  as  indicated  in  the  data  record,  state  the  law  of  lengths. 

Questions,  a.  From  the  mean  time  of  one  vibration  of  the  three  trials  made  with  the  long  pendulum 
using  a  small  arc,  and  from  the  measured  length  of  this  pendulum,  compute  with  the  aid  of  the  proportion- 
ality shown  in  II  the  length  of  a  pendulum  which  will  beat  seconds. 

b.  It  is  shown  in  more  advanced  work  in  physics  that  the  period  of  a  pendulum  t  in  terms  of  its  length 

I  and  the  value  of  the  acceleration  g  due  to  gravity,  is  given  by  the  equation  t  =  TT xl—  •    Using  the  period 
and  length  of  the  first  pendulum,  compute  g  for  your  locality. 

c.  If  the  square  of  the  period  is  directly  proportional  to  the  length  of  the  pendulum,  what  kind  of  a 
graph  would  be  obtained  by  plotting  the  squares  of  the  periods  for  several  pendulums  as  horizontal  dis- 
tances and  the  corresponding  lengths  as  vertical  distances  ?   If  time  permits,  verify  your  answer  by  plotting 
your  own  data  in  that  way. 

*  If  the  second  hand  is  observed  through  a  reading  glass  of  moderate  power  or  the  linen  tester  of  Exp.  47,  it  will  b* 
found  easy  to  estimate  fifths  of  a  second. 

[311 


I.  (a)  Effect  of  amplitude 


EXPERIMENT  12    (Continued) 
RECORD  OF  EXPERIMENT 


ARC  10  CM. 

TIME  OF  BEGINNING 
COUNT 

TIME  OF  ENDING 
COUNT 

TIME  OF  ONE 
TOTAL  TIME                VIBRATION 

Sample  trial 
First  trial 

IQh  45m  10.4* 

10h  47m.  25.0s 

134.68                      1.3408 

Second  trial 

Third  trial 

Mean          =          

ARC  30  CM. 
First  trial 

Second  trial 

Mean          =    

ARC  200  CM. 
First  trial 

(&)  Effect  of  different  weight 

II.  Relation  between  lengths  and  periods 

Length  of  pendulums,  No.  1  = cm.,  No.  2  = cm.,  No.  3  = 

Period  of  pendulums,   No.  1  = sec.,  No.  2  = sec.,  No.  3  = 


Length  No.  1  _        /Period  No.  1\2^  Length  No.  1  _        /Period  No.  1\2_ 

Length  No.  2  ~    '   \Period  No.  2/  ~  Length  No.  3  ~    '   (.Period  No.  3/  ~ 


.cm. 
sec. 


[32] 


EXPERIMENT  13 


PIG.  27 


RELATION  BETWEEN  FORCE  ACTING  UPON  AN  ELASTIC  BODY  AND  THE 
DISPLACEMENT  PRODUCED  (HOOKE'S  LAW) 

I.  Stretching.    Set  up  a  steel  spring  S  and  a  mirror-scale  M,  in  the  manner  shown  in  Fig.  27. 
Take  the  reading  of  the  index  upon  the  scale  when  only  the  weight  holder  hangs  from  the  spring. 

In  so  doing  place  the  eye  so  that  the  image  of  the  tip  of  the  pointer  p,  as  seen  in  the  mirror,  is  exactly 
in  line  with  the  tip  of  the  pointer  itself.  Record  the  position  at  which  the  line  cf  sight  crosses  the 
mirror  scale,  reading  to  the  nearest  tenth  millimeter  (this  tenth-millimeter  place  being, 
of  course,  an  estimate). 

Increase  the  weight  upon  the  pan  100  g.  at  a  time  until  it  has  reached  a  total  of 
400  g.,  and  take  the  reading  on  the  scale  after  each  addition. 

Then  remove  the  weights  100  g.  at  a  time  and  take  the  corresponding  readings. 

II.  Bending.    Set  up  the  mirror  scale  behind  the  middle  of  a  thin  wooden  or  steel 
rod  supported  as  in  Fig.  28  and  take  again  a  set  of  readings  like  those  in  I,  the  index 
being  now  the  point  of  a  pin  stuck  with  wax  to  the  middle  of  the  rod. 

Finally,  show  graphically  the  relation  between  displacement  and  the  force  produc- 
ing it.  Let  distances  along  OX,  that  is,  to  the  right  of  the  origin  0  of  the  graph, 
represent  forces,  and  distances  along  OF,  that  is,  above  the  origin  0  of  the  graph, 
represent  displacements.  Choose  the  scales  used  so  that  the  graphs  nearly  fill  the 
page  of  coordinate  paper.  Plot  both  sets  of  data  on  the  same  sheet. 

With  a  straightedge  draw  two  straight  lines  through  the  origin  0,  which  shall 
come  nearest  to  all  the  points.  Why  do  these  graphs  *  pass  through  the  origin  ? 

State  in  your  own  words  in  the  notebook  the  law  which  the  above  study  of  two  different  sorts  of 
elastic  displacement  has  shown  to  exist  between  the  distorting  force  F  and  the  displacement  D  which 
this  force  produces. 

State  this  result  in  the  form 
of  an  equation. 

III.  Substitute     for     I.      (The 
spring  balance.)  With  a  centimeter 
rule  measure  the  distance  from  the 
zero  to  the  500-g.  mark  on  the  bal- 
ance, from  the  zero  to  the  1000-g. 
mark,  etc. 

What    relation    do    you    find 
exists  between  the   distance  the  spring  in  the  balance  is  stretched  and  the  stretching  weight? 

Plot  the  result  of  these  observations,  letting  distances  along  OX  represent  the  stretching  forces, 
and  distances  along  OY  the  corresponding  elongations  of  the  spring. 

How  would  you  proceed  to  graduate  a  spring  balance  that  had  no  marks  on  it  so  that  it  would 
read  in  grams  ? 

Would  a  spring  balance  graduated  at  sea  level  give  correct  readings  if  taken  to  the  top  of  a  high 
mountain  ?  Why  ? 

How  would  the  readings  of  a  spring  balance  be  affected  if  it  were  taken  from  sea  level  at  the 
equator  to  sea  level  at  the  north  pole  ?  Why  ? 

*  If  the  spring  has  an  initial  "set"  due  to  the  twist  in  the  wire  as  the  spring  is  coiled  when  made,  the  pan  should  be 
heavy  enough  to  stretch  it  sufficiently  to  make  a  slight  space  between  adjacent  turns,  otherwise  the  graph  will  not  pass 
through  the  origin.  Why  ? 

[33] 


FIG.  28 


EXPERIMENT  13    (Continued) 
RECORD  OF  EXPERIMENT 


I 

II 

III 

Spring 

Differences 

Rod 

Differences 

Marks  on  Balance 

Distance 

Pan  reading     —  

0  to    500  g. 

cm. 

100-g  reading  =  

0  to  1000  g. 

cm. 

900-g.  reading  =  

0  to  1500  g. 

cm. 

300-g.  reading  =  .. 

0  to  2000  g. 

.  cm. 

400-g.  reading  =  

300-g.  reading  =  

200-g.  reading  =  .. 

100-g.  reading  =  ... 

Pan  reading     =  ... 

[34] 


EXPERIMENT  14 


THE  PRESSURE  COEFFICIENT  OF  EXPANSION  OF  A  GAS  AND  THE 
MEANING  OF  ABSOLUTE  ZERO 

Experiments  14  and  14  A  are  intended  as  alternatives,  the  choice  depending  upon  equipment. 
It  is  interesting,  however,  to  have  a  part  of  the  class  perform  14  and  a  part  14  A,  and  then  to  let 
them  compare  results. 

Charles  found  that  when  a  body  of  gas  is  heated  in  a  closed  vessel  the  volume  of  which  is  kept 
constant,  the  pressure  which  the  gas  exerts  against  the  walls  of  the  vessel  increases  as  the  temperature 
rises.  The  ratio  between  the  increase  in  pressure  per  degree  and  the  pressure  which  the  gas  exerts  at 
0°  C.  is  called  the  pressure  coefficient  of  expansion  of  the  gas.  For  example,  if  Pt  rep- 
resents the  pressure  at  a  temperature  of  t°  C.  and  PO  the  pressure  at  0°C.,  then  the 

P 


=1  s 


and 


FIG.  29 


increase  in  pressure  has  been  Pt  —  PQ,  the  increase  per  degree  has  been 
the  pressure  coefficient  c  is  this  increase  divided  by  P0.    Thus, 

P—  P 
c  =  ^—^. 

0 

To  find  this  coefficient  experimentally,  first  read  the  barometer.  Then,  before 
attaching  the  bulb  B,  adjust  the  arms  a  and  b  (Fig.  29)  until  the  mercury  in  each 
stands,  say,  5  cm.  above  the  bottom  of  the  scale  S,  the  distance  from  the  bottom 
of  S  to  the  point  of  attachment  of  the  rubber  tubing  to  the  arm  b  being  at  least 
30  cm.  and  the  distance  from  the  mercury  surface  in  a  to  the  scratch  m  on  the 
tube  a  being  about  4  cm. 

Now  introduce  about  1  or  2  cc.  of  phosphorus  pentoxide  into  B  to  keep  the 
air  in  B  perfectly  dry ;  then  attach  B,  as  in  the  figure,  with  a  bit  of  thick- walled  gum- 
rubber  tubing  and  pack  wet  snow  or  crushed  ice  about  it  in  a  vessel  V  until  B  is  completely  covered. 

Raise  the  arm  b  until  the  mercury  in  a  is  just  opposite  the  scratch  m,  tapping  a  gently  with  a  pencil 
to  prevent  the  mercury  from  sticking.  Wait  two  or  three  minutes  to  make  sure  that  the  air  in  B  has 
reached  the  temperature  of  the  ice,  and  then  adjust  again  to  the  scratch  m  and  read  on  the  scale  S 
the  levels  in  both  a  and  b. 

Put  the  bulb  into  the  steam  generator  shown  in  Fig.  31,  and  boil  the  water.  Adjust  the  arm  b 
until  the  level  in  a  is  again  at  m ;  tap  and  again  read  the  levels  of  the  mercury  in  a  and  b. 

Immediately  after  this  reading  lower  the  arm  b  to  its  first  position,  so  that  the  mercury  may  not  be  drawn 
over  into  B  as  the  bulb  cools. 

From  your  data  compute  c,  as  indicated  in  the  data  record. 

State  in  your  own  way  in  your  notebook  what  the  "  pressure  coefficient  of  expansion  e  "  means. 

Questions,  a.  What  per  cent  of  error  would  have  been  introduced  into  your  numerator,  P100  —  PO,  and 
therefore  into  your  result,  by  an  error  of  half  a  millimeter  in  this  increase  in  pressure  when  the  gas  is  heated  ? 

b.  If  the  boiling  point  of  water  on  the  day  of  your  experiment  were  99.5°  instead  of  100°,  what  per  cent 
of  error  would  you  have  introduced  into  your  result  by  calling  it  100°?    On  the  whole  is  your  result  as  ac- 
curate as  you  could  have  expected,  in  view  of  such  sources  of  error  as  you  can  see  ? 

c.  If  a  gas  at  0°  C.  is  cooled  at  constant  volume,  and  if  the  pressure  decreases  5fg-  of  what  it  was  at  0°  C. 
for  each  degree  cooled,  how  many  degrees  would  it  have  to  be  cooled  to  reduce  the  pressure  to  nothing  ? 

d.  At  this  temperature  would  the  molecules  be  in  motion  ?    Explain  what  absolute  zero  means. 

e.  Show  from  your  results  in  this  experiment  that  when  a  gas  is  heated  at  constant  volume,  the  pressure 

P        f     |    27S       T 
is  directly  proportional  to  the  absolute  temperature ;  that  is,  — -  =  1  |   07Q  =  -^  (Charles's  law). 

[351 


EXPERIMENT  14   (Continued) 

RECORD  OF  EXPERIMENT 

Barometer  reading          = cm. 

Reading  in  a  at  0°  C.      =  cm."]   Difference  = cm. 

Reading  in  b  at  0°  C.       =  cm.J   .-.  P0  = cm. 

Reading  in  a  at  100°  C.  =  cm."j   Difference  = cm. 

Reading  in  b  at  100°  C.  =  cm.J   .-.  P100         =  cm. 

C  =  PIW>  ~  P°  =  =  —J— .        Accepted  value  =  .00367  =  ,| ff.         Per  cent  of  error  = 


[36] 


EXPERIMENT  14  A 


THE  VOLUME  COEFFICIENT  OF  EXPANSION  OF  A  GAS  (GAY-LUSSAC'S  LAW) 

Gay-Lussac  found  that  when  a  confined  body  of  gas  is  kept  under  constant  pressure  and  heated, 
its  volume  increased  at  the  same  rate  at  which  its  pressure  increased  when  the  volume  was  kept 
constant  (see  Exp.  14). 

When  a  confined  body  of  gas  is  kept  under  constant  pressure  and  heated,  it  follows,  from  Boyle's 
law,  that  its  volume  must  increase  at  the  same  rate  at  which  its  pressure  would  increase  if  the  volume 
were  kept  constant.  The  ratio  between  the  increase  in  volume  per  degree  and  the 
volume  at  0°  C.  is  called  the  volume  coefficient  of  expansion ;  that  is,  if  V  and  V 
represent  the  volumes  at  100°  C.  and  0°  C.  respectively,  then  the  volume  coefficient 
c  is  given  by  the  equation 


c  = 


V    —  I 

'  100  r 

100  v 


This  coefficient  may  be  defined  as  the  expansion  at  0°  0.  per  cubic  centimeter  per 
degree.  It  should  be  the  same  as  the  pressure  coefficient  discussed  above. 

To  find  it  experimentally,  let  a  thread  of  dry  air  about  20-25  cm.  long  be  con- 
fined by  a  mercury  index  2  or  3  cm.  long  in  a  piece  of  barometer  tubing  which  is 
sealed  at  one  end  and  is  about  40  cm.  long.*  (See  Fig.  30.) 

First  measure  carefully  and  record  the  length  BC  of  the  mercury  index  and  the 
total  length  AD  of  the  bore,  allowing  as  best  you  can  for  the  fact  that  the  bore  is 
not  quite  uniform  very  near  the  closed  end.  Then  stand  the  tube  upright,  closed 
end  down,  in  a  battery  jar,  and  pack  wet  snow  about  it  up  to  the  index.  Tap  the 
tube  with  a  pencil,  and,  when  the  index  remains  constant,  measure  from  A  to  the  top 
B  of  the  index.  Remove  the  tube  and  push  it  through  the  hole  in  the  cork  which 
closes  the  steam  generator  of  Figs.  31  and  41.  After  the  steam  has  been  issuing 
from  the  upper  vent  for  a  minute  or  two  adjust  the  height  of  the  tube  in  the  cork 
so  that  the  upper  end  of  the  index  is  just  on  a  level  with  the  top  of  the  cork,  and 
then  measure  from  A  to  the  top  of  the  cork.  Since  the  tube  is  of  approximately 
uniform  bore,  you  may  take  the  difference  between  the  last  two  measurements  as 
F100  —  VQ.  From  the  first  three  readings  find  the  length  of  the  thread  of  air  at  0°  C. 
and  call  it  VQ.  Compute  c  from  your  data. 

Questions,  a.  Is  your  error  larger  than  would  be  accounted  for  by  an  error  of,  say, 
.5  mm.  in  measuring  Vm  —  F0  ? 

If  so,  it  is  probable  either  that  the  bore  is  not  uniform  or  that  the  confined  air  is  not 
thoroughly  dry. 

b.  Show  from  the  results  of  this  experiment  that  when  a  gas  is  heated  at  constant  pressure  the  volume 
is  directly  proportional  to  the  absolute  temperature ;  that  is, 

F!      fj  4-  273       7\ 


FIG.  30 


c.  If  Exp.  9  (Boyle's  law)  was  performed  at  20°  C.,  what  would  have  been  the  value  of  the  constant  PV 
had  the  experiment  been  performed  at  25°  C.? 

*  To  make  such  tubes,  take  barometer  tubing  of  about  1.5-mm.  bore,  clean  it  with  hot  aqua  regia  or  a  hot  solution  of 
potassium  bichromate  in  strong  sulphuric  acid,  then  rinse  with  distilled  water,  and  dry  by  gently  heating  while  a  current  of 
air  passes  first  through  a  calcium-chloride  drying  tube  and  then  through  the  barometer  tube.  Seal  one  end  quickly  in  a  Bun- 
sen  burner,  and  with  a  capillary  funnel  introduce  the  thread  of  mercury  BC.  Attach  the  cotton-  and  calcium  chloride-tube  to 
keep  the  inside  of  the  tube  dry,  and  the  tube  should  work  satisfactorily  for  months.  If  the  drying  tube  is  not  used,  moisture 
will  work  past  the  mercury  thread  as  it  moves  back  and  forth. 

[37] 


EXPERIMENT  14  A    (Continued) 

RECORD  OF  EXPERIMENT 

Length  of  index,  EC  = cm. 

Length  of  bore,  AD  — cm. 

From  A  to  index  at  0°C.,  AB0         = cm. 

From  A  to  index  at  100°  C.,  ^4-B100  =  ...% cm. 

^100  ~  1ro  =  AB0  —  AB100  =  cm. 

F0  =  AD  -  (AB0  +  BC)  = cm. 

C  =     v>°  ~  T  «  =  ...  ...  =  — — .        Accepted  value  =  .00367  =  ,.1*.        Per  cent  of  error  = 

100  Vn  *'J 


[38] 


EXPERIMENT  15 


COEFFICIENT  OF  EXPANSION  OF  BKASS 

The  linear  coefficient  of  expansion  of  a  solid  is  equal  to  that  fractional  part  of  its  length  which  it 
increases  when  heated  1°  C.  The  coefficient  of  expansion  of  brass  is  .0000187;  this  means  that  a  foot 
of  brass  rod  will  increase  .0000187  ft.  in  length  when  heated  1°  C.,  or  that  1  cm.  will  increase 
.0000187  cm.  in  length  when  heated  1°  C.,  etc. 

Thus,  if  /2  represents  the  length  at  a  temperature  t^  and  ^  at  a  temperature  tf  the  increase  in  length 

per  degree  is •>  and  the  fractional  part  which  this  is  of  the  length  is  the  linear  coefficient  of 

2~     1 


expansion  k.    Thus, 


7.  __ 


A  shallow  transverse  groove  is  filed  at  some  point  c  (Fig.  31)  near  one  end  of  a  piece  of  brass 
tubing  oc  about  a  meter  long  and  a  centimeter  in  diameter. 

Place  this  tube  upon  two  wooden  blocks  A  and  B  so  that  the  groove  rests  upon  a  sharp  metal  edge 
attached  to  A  while  the  other  end  is  supported  by  a  piece  of  glass  or  brass  tubing  b  about  6  mm.  in 
diameter,  which  in  turn  rests  upon  a  smooth  glass  plate  waxed  to  the  top  of  B.  To  one  end  of  the 
glass  rod  b  a  pointer  p  about  20  cm. 
long  is  attached  by  means  of  seal- 
ing wax.  When  the  brass  tube  oe 
is  heated,  its  expansion  causes  b  to 
roll  forward,  and  this  produces  a 
motion  of  the  end  of  the  pointer  p 
over  the  mirror  scale  s. 

Attach  the  tube  oc,  as  in  the  fig-  FlG  31 

ure,  to  a  steam  boiler  containing 
at  first  only  cold  water.     Then  insert  a  thermometer  into  the  open  end  o  of  the  brass  tube  oc. 

Give  the  thermometer  three  or  four  minutes  to  take  up  the  temperature  of  the  tube ;  then  read 
and  record,  and  replace  it  in  o. 

Measure  with  a  meter  stick  the  distance  between  the  knife-edge  c  and  the  middle  of  the  rod  b. 
all  this  length  7^ 

Record  the  position  of  the  tip  of  the  pointer  upon  the  mirror  scale  «,  estimating  very  carefully  to 
nths  of  a  millimeter.    Call  this  reading  S^    In  taking  this  reading,  sight  (as  always)  across  the 
image  of  the  pointer  and  the  pointer  itself. 

Apply  heat  to  the  boiler  until  steam  passes  rapidly  through  the  tube.  If  the  current  of  steam  is 
sufficiently  strong,  the  brass  tube  will  not  need  a  nonconducting  covering.  Nevertheless  it  is  generally 
advisable  before  beginning  the  experiment  to  roll  up  a  paper  tube  about  1£  cm.  in  diameter,  and  to 
slip  it  over  the  tube  between  c  and  b  in  order  to  minimize  heat  losses. 

After  steam  has  been  issuing  from  o  for  one  or  two  minutes,  take  again  the  reading  of  the 
pointer  p  upon  the  scale  s.  Call  this  reading  S2. 

Take  the  reading  of  the  thermometer  as  it  lies  in  the  tube  surrounded  by  the  steam  escaping  from  <?. 

Measure  with  the  meter  stick  the  length  of  the  pointer  p  from  its  tip  to  the  middle  of  b. 

Measure  with  the  micrometer  caliper  the  diameter  of  6,  taking  readings  upon  at  least  three 
different  diameters.  This  measurement  should  be  made  with  an  accuracy  of  at  least  .01  mm.  If  the 
calipers  are  not  available,  wrap  a  fine  linen  thread  ten  or  twenty  times  around  5,  measure  the  length 
of  the  thread,  and  from  this  compute  the  diameter. 

[39] 


: 


EXPERIMENT  15    (Continued) 

From  Fig.  32  it  will  be  seen  that  at  any  given  instant  the  rod  b  is  rotating  about  the  lower  end 
of  its  own  vertical  diameter,  and  that  while  the  upper  end  of  this  diameter  is  moved  a  distance  (12  —  Z:), 
the  pointer  p  moves  through  the  same  angle  over  the  distance  ($2  —  S^).  Then  from  similar  triangles, 


p  p 

Using  this  value  of  (72  —  ^),  compute  k. 

In  calculating  be  sure  that  you  express  all 
length  measurements  in  the  same  units ;  that  is,  all 
in  centimeters. 

Questions,  a.  The  observational  errors  in  this  experiment  amount  to  about  2%.  Are  your  results  as 
accurate  as  you  should  expect  ? 

6.  If  a  cube  of  brass  1  dm.  on  a  side  is  heated  1°  C.,  what  will  be  its  volume  ?  what  is  the  increase  in 
volume  ?  what  is  the  volume  coefficient  of  expansion  of  brass  ? 

c.  What  relation  do  you  see  between  the  volume  and  the  linear  coefficients  of  expansion  ? 

d.  How  are  wagon  tires  put  on  a  wooden  wheel  to  make  them  very  tight  ? 


Length  of  cb,  or  lt  = 

First  temperature  of  rod,  ^  = 

Second  temperature  of  rod,  <2  = 
First  reading  on  scale,  St 

Second  reading  on  scale,  S2  = 

Diameter  of  &  = 
Length  of  pointer,  p 


RECORD  OF  EXPERIMENT 

,  ..............  cm. 


cm. 

cm. 

cm. 

.  cm. 


Accepted  value  =  .0000187.         Per  cent  of  error  = 


[40] 


EXPERIMENT  16 


FIG.  33 


(D 


THE  PRINCIPLE  OP  MOMENTS 

Slip  the  meter  bar  AB  through  the  sliding  knife-edge  support  C  (Fig.  33)  until  it  will  rest  exactly 
horizontally  when  the  knife-edge  rests  upon  the  glass  surfaces  of  the  wooden  frame/.  See  that  C  is 
clamped  firmly  to  the  bar,  read  the  position  of  the  knife-edge  on  the  bar,  and  then  proceed  as  follows : 

(a)  By  means  of  thread  hang  a  100-g.  weight  W^  from  a  point  near  one  end  of  the  beam  and  find 
the  point  at  which  a  200-g.  weight  Wz  must  be  hung  on  the  other  side  in  order  that  the  bar  may  rest 
again  in  an  exactly  horizontal  posi- 
tion.   Take   the   product  of  each 
weight  by  its  distance   from   the 
fulcrum.  What  relation  do  you  dis- 
cover between  these  two  moments  ? 
(The  product  of  a  force  by  the  lever 
arm  on  which  it  acts  is  called  the 
moment  of  the  force.) 

(5)  Hang  two  weights,  say  a 

100-g.  weight  W1  and  a  50-g.  weight  W2,  at  different  points  on  the  left  side  of  the  fulcrum  and  not 
too  close  to  it,  and  then  balance  the  lever  by  hanging  a  200-g.  weight  W%  at  the  proper  point  on  the 
other  side.  Compare  the  sum  of  the  moments  of  W1  and  W2  with  the  moment  of  W&. 

(c)  Hang  some  unknown  weight  X  from  a  point  near  the  left  end  at  a  distance  I  from  the  fulcrum, 
and  balance  it  by  a  known  weight  W  hung  at  the  proper  point  on  the  other  side.  By  applying  the 
principle  of  moments,  which  you  learned  in  (a)  and  (5),  find  the  value  of  X.  Weigh  it  on  the  balance 
and  compare  the  two  results. 

(<f)  Hang  from  different  points  on  the  left  side  an  unknown  weight  X  and  a  known  weight  W^ 
and  balance  by  two  known  weights  Ws  and  Wt  placed  at  different  points  on  the  other  side.  Let  I 
represent  the  distance  of  X  from  the  fulcrum.  Compute  the  weight  of  the  unknown  body  and  compare 
with  the  result  of  a  direct  weighing. 

(e)  Slip  the  knife-edge  C  to  some  point  0  such  that  00  is  10-15  cm.,  and  clamp.  Slip  a  known 
weight  W,  say  200  g.,  along  between  0  and  B  until  the  beam  rests  horizontally  when  placed  in  the 
support.  Then  by  applying  the  principle  of  moments  find  the  weight  of  the  beam  on  the  assumption 
that  the  whole  effect  of  the  earth's  attraction  on  the  beam  is  equivalent  to  one  single  force  equal  to 
the  whole  weight  of  the  beam  and  applied  at  the  first  position  of  the  knife-edge;  that  is,  at  (7,  the 
center  of  gravity  of  the  beam. 

K  X  represents  the  weight  of  the  beam,  the  principle  of  moments  then  gives 

X  x  distance  CO  =  known  weight  x  its  distance  from  0. 
Compare  the  result  with  a  direct  weighing  of  the  beam. 

Questions,    a.  State  what  general  conclusion  you  are  able  to  draw  from  (a)  and  (&). 
&.  State  what  method  the  experiments  have  shown  you  for  finding  the  weight  of  any  body  without  the 
aid  of  a  pair  of  scales. 

c.  Where  does  the  result  of  (e)  show  that  the  total  weight  of  a  body,  that  is,  the  sum  of  the  forces  of 
gravity  which  act  upon  its  particles,  may  be  considered  as  concentrated  ? 

d.  A  gate  14  x  5  ft.,  weighing  100  lb.,  is  supported  at  the  end  by  two  hinges  4  ft.  apart.    What  is  the 
pull  on  the  upper  hinge  in  pounds  ?   (Apply  principle  of  moments ;  consider  center  of  gravity  of  gate  at  the 
center  of  the  gate.) 

e.  If  a  boy  weighing  100  lb.  stands  on  the  end  of  the  gate,  what  will  then  be  the  pull  on  the  upper  hinge  ? 


(a) 


EXPERIMENT  16    (Continued) 

RECORD  OF  EXPERIMENT 

;  its  lever  arm  =  ........................  ;  its  moment  =  ........................  "|     per  cent  of  differ- 


W2  =  ;  its  lever  arm  = ;  its  moment  = 

)    Wl  = ;  its  lever  arm  = ;  its  moment  = 

W2  = ;  its  lever  arm  =  ;  its  moment  = 

fper  cent  of  differ- 

•  W«  = ;  its  lever  arm  =  ...  :  its  moment  = ;  •<  r 

I     ence  =  


:  sum      = 


(c)   W  = ;  its  lever  arm  = ;  its  moment  = 

I      = ;  .•.  X  = ;  by  direct  weighing  X 

(dy   Ws  = ;  its  lever  arm  = ;  its  moment  = 

Wt  = ;  its  lever  arm  = ;  its  moment  = 

W^  = ;  its  lever  arm  =  ;  its  moment  = 

/       =  ;  .-.  X  = ;  by  direct  weighing  X  .    = 

(ey  Reading  of  knife-edge,  at  C  = ;  at  0    = ;      .-.  OC  = 

W  =  ;  its  lever  arm  = ;  its  moment  = 

OC  x  X  = ;  .-.  X  = ;  by  direct  weighing  X  = 


[42] 


EXPERIMENT  17 


THE  PBINCIPLE  OF  WOEK  AND  THE  EFFICIENCY  OF  THE  INCLINED  PLANE 

I.  Principle  of  work.   Since  the  work  which  a  force  accomplishes  is  equal  to  the  product  of  the 
force  by  the  distance  through  which  it  moves  the  point  upon  which  it  acts,  the  work  done  by  a  force 
F  (Fig.  34)  in  moving  a  mass  a  distance  I  (=  on)  up  the  inclined  plane  on  is  equal  to  Fl.    But  the 
work  done  against  gravity  is  equal  to  the  product  of  the  weight  W  which  is  moved  tunes  the  vertical. 
height  h  (=  mn)  through  which  W  has  been  raised. 

The  object  of  this  experiment  is  to  find  what  relation  would 
exist  between  the  work  Fl  of  the  acting  force  and  the  work  Wh 
of  the  resisting  force,  in  case  there  were  no  friction. 

First  weigh  the  car  to  be  used  on  the  inclined  plane.  Call 
this  weight  C. 

Then  with  the  inclined  plane  set  at  an  angle  of  approxi- 
mately 45°,  hang  enough  100-g.  weights  at  F  to  pull  the  car 
up  the  incline. 

Now  add  weights,  from  a  set  of  weights, 
to  the  car  until,  with  continued  slight 
tapping  on  the  plane,  the  car  will  just 
move  slowly  and  uniformly  down.  Call  the 
weights  in  the  car  wl  . 

Remove  weights  until,  with  like  tap- 
ping, the  car  moves  just  as  uniformly  up. 
Call  the  weights  in  the  car  wz. 

Take  the  mean  of  C  +  wl  and  C  +  w2  as 
the  weight  W,  which  the  force  F  would  sup- 
port  on  the  plane  if  there  were  no  friction. 

Measure  carefully  with  a  meter  stick  the  height  of  the  plane  mn  and  call  it  h.  Similarly,  measure 
the  length  of  the  plane  on  and  call  it  I. 

Set  the  inclined  plane  at  an  angle  of  about  30°  and  repeat  all  observations. 

State  in  words  the  principle  of  work  as  proved  by  your  data.  Give  also  the  algebraic  statement  of 
this  principle  for  the  inclined  plane. 

II.  Efficiency  of  the  inclined  plane.    The  efficiency  of  any  machine  is  the  ratio  of  the  useful  work 

accomplished  to  the  work  done  by  the  acting  force  ;  that  is,  efficiency  =  -  -  —  •    This  is  always  less 

input 

than  100  %,  since,  on  account  of  friction,  the  output  of  all  machines  is  less  than  the  input. 

In  the  case  of  the  inclined  plane,  therefore,  the  efficiency  in  terms  of  the  data  already  taken  is 

given  by  the  formula  (  C  +  w  2)  h 

Efficiency  =  *  -  j~~  ' 

Compute  the  efficiency  for  both  trials,  and  record. 

Questions,  a.  Two  horses  pull  a,  loaded  wagon  weighing  3960  Ib.  up  a  5  %  grade  (one  that  rises  1  ft. 
in  20  ft.),  1000  ft.  long,  in  5  min.  If  the  force  exerted  by  each  horse  is  165  Ib.,  what  is  the  efficiency  ?! 

&.  In  a  how  many  foot  pounds  of  work  does  each  horse  do  per  minute  ?  This  is  the  rate  at  which  the 
average  horse  can  work  as  found  by  James  Watt  (1736-1819). 

c.  In  a  if  the  load  had  been  pulled  in  a  car  with  ball-bearing  wheels,  on  a  steel  track,  how  would  the 
efficiency  be  affected  ? 

d.  State  two  things  which  affect  the  efficiency  of  an  inclined  plane. 

[43] 


FlG- 


I.  Principle  of  work 


II.  Efficiency 


EXPERIMENT  17    (Continued) 
RECORD  OF  EXPERIMENT 


1 

TRIAL, 

c 

wl 

wt 

W 

h 

f 

I 

Fxl 

Wx  h 

PER  CENT  OF 
DIFFERENCE 

1 

2 

TRIAL 

OUTPUT 
(C+  wj  h 

INPUT 
JFxl 

EFFICIENCY 

1 

2 

[44] 


EXPERIMENT  17  A 


III(i) 


111(2) 


F' 


THE  USE  OF  PULLEYS  TO  CHANGE  THE  DIRECTION'  OF  A  FORCE,  TO 
MULTIPLY  FORCE,  AND  TO  MULTIPLY  SPEED 

I.  The  single  fixed  pulley.  With  a  piece  of  fish  line  or  common  cord  hang  a  weight  F'  (the  resist- 
ance) of  about  1  or  2  kg.  over  the  pulley,  as  shown  in  /  (Fig.  35). 

(a)  Lift  the  weight  by  pulling  uniformly  and  slowly  down  on  the  hook  of  the  balance,  taking  its 
reading  as  you  do  so.  Add  to  this  reading  the  weight  of  the  balance,  to  get  F  (down).  In  a  similar 
way  obtain  F  (up).  The  average 
of  F  (down)  and  F  (up)  gives  what 
the  force  would  be  without  friction. 
Denote  this  by  F. 

(5)  How  far  does  the  acting 
force  F  (the  effort)  move  to  lift  the 
weight  F'  (the  resistance)  10  cm.  ? 
These  distances  are  called  S  and 
S'  respectively. 

(<?)  Compute  F  x  S  and  F'  X  S' ; 
F'+F  and  S+S'\  and  the  effi- 
ciency, or  (F'  x  £')  -r-  (F  (down) 
X  £),  that  is,  output  -f-  input. 

(cT)  From  the  relation  between 
F  x  S  and  F'  x  S'  state  the  prin- 
ciple of  work.  FlG  35 

(e)  The  quotient  F'  +  F,  that 

is,  the  ratio  of  the  resistance  to  the  effort,  is  called  the  mechanical  advantage.    State  in  your  record 
two  other  ways  of  finding  the  mechanical  advantage  of  a  system  of  pulleys. 

II.  The  single  movable  pulley.   Take  a  set  of  observations  similar  to  those  of  I,  (a)  and  I,  (5), 
using  the  pulley  as  arranged  in  II  (Fig.  35).    In  this  case,  however,  do  not  add  the  weight  of  the 
balance  to  the  balance  reading  to  get  F  (down)  or  F  (up).    Add  the  weight  of  the  pulley  to  that  of 
the  mass  lifted,  to  get  F'. 

III.  Using  a  block  and  tackle  similar  to  that  shown  in  777  (.?)  or  III  (#)  of  Fig.  35,  make  with  its 
aid  observations  and  computations  like  those  in  I. 

IV.  Hang  a  small  weight,  say  100  g.,  on  the  free  end  of  the  string  of  ///  (./)  at  F  (Fig.  35),  and 
with  the  hand  pull  down  at  F'  instead  of  using  the  weight  F'.    Is  the  mechanical  advantage  now  equal 

to  the  number  of  strands  n  leaving  the  movable  pulley,  or  is  it  -  ? 

fv 

With  this  arrangement  is  it  force  or  speed  that  is  multiplied  ? 

Which  is  multiplied  when  the  mechanical  advantage  is  less  than  1  ?  Which  is  multiplied  when  the 
mechanical  advantage  is  greater  than  1  ? 

Questions,  a.  Will  it  take  more  or  less  work  to  hoist  a  heavy  weight  to  the  top  of  a  high  building  with 
a  block  and  tackle  than  to  lift  it  directly  from  above  with  a  single  rope  attached  ?  Why  is  the  block  and 
tackle  used? 

6.  Draw  a  diagram  in  your  book  of  a  block  and  tackle  whose  mechanical  advantage  is  4 ;  of  one  used  so 
that  its  mechanical  advantage  is  £. 

c.  Why  is  the  efficiency  of  a  pulley,  or  of  a  system  of  pulleys,  always  considerably  lower  than  that  of 
a  lever  or  of  a  system  of  levers  ? 

[45] 


EXPERIMENT  17  A   (Continued) 
RECORD  OF  EXPERIMENT 


Data 

Weight  of  balance 
Weight  of  single  pulley 
Weight  of  block  and  tack! 

=  er. 

g- 
ff. 

e  = 

FfDOWX) 

FQJp) 

F 

8 

& 

S' 

I 

10  cm. 

II 

10  cm. 

III 

10  cm. 

Calculations 


PRINCIPLE  OF  WORK 

MECHANICAL  ADVANTAGE 

EFFICIENCY 
fS'+FQowiQxS 

fx  S 

F'xS' 

P+F 

S+S' 

Number  of  Support- 
ing Strands 

I 

II 

* 

III 

*  In  this  case  efficiency  =  F'S'  -f-F(up)  x  8,  since  the  effort  F  acts  up  in  overcoming  the  resistance  F', 


[46] 


EXPERIMENT  18 


FIG.  36 


WHEN  ONE  CUBIC  FOOT  OF  THE  GAS  PRODUCED  BY  YOUR  HOME  GAS  COMPANY 
IS  BURNED,  HOW  MUCH  HEAT  IS  PRODUCED  BY  THE  COMBUSTION? 

First  attach  tube  A  of  Fig.  36  to  the  gas  main.  Then,  in  order  that  you  may  be  sure  of  complete 
combustion,  adjust  the  Bunsen  burner  until,  when  burning  low,  the  air  supply  is  sufficient  to  make  it 
burn  with  a  rustling  sound  and  a  blue  flame.  When  satisfactorily  adjusted,  record  the  reading  of  the 
water  manometer  G. 

To  fill  the  improvised  gas  meter 
of  Fig.  36  remove  the  weight  W 
from  the  top  of  the  gas  container, 
close  stopcock  C',  open  (7,  and  allow 
the  gas  to  enter  until  the  meter  is 
filled. 

Now  attach  tube  A  to  C",  re- 
place the  weight  W,  and  open  C' 
until,  with  the  burner  lighted,  the 
manometer  G  reads  the  same  as 
before. 

Then  place  the  burner  under  some  form  of  Junker  calorimeter  and  adjust  the  flow  of  water  until 
the  temperature  of  the  outflowing  water  is  about  as  much  above  the  temperature  of  the  room  as  that 
of  the  inflowing  water  is  below  the  temperature  of  the  room.  As  soon  as  the  temperature  of  the  out- 
flowing water  is  constant  and  just  as  the  gas  meter  reads  some  tenth  of  a  cubic  foot,  as  read  on  the 
scale  S,  note  the  reading  of  the  gas  meter  and  hi  the  same  instant  place  a  pail  under  the  outflow  of 
the  calorimeter. 

Record  the  temperatures  of  both  the  inflowing  and  the  outflowing  water  about  every  minute  during 
the  time  of  the  experiment. 

When  1  cu.  ft.  of  gas  has  been  consumed,  remove  the  pail  from  under  the  outflow  of  the  calorim- 
eter, at  the  same  instant  reading  the  gas  meter. 

NOTE.   It  probably  will  be  found  more  convenient  to  use  less  than  a  cubic  foot  of  gas. 

From  the  weight  of  the  water  and  its  rise  in  temperature  as  it  passed  through  the  calorimeter 
compute  how  much  heat  is  produced  by  the  combustion  of  1  cu.  ft.  of  the  gas  used. 

Quantities  of  heat  are  measured  in  either  British  Thermal  Units  (B.T.U.)  or  in  calories. 

A  British  thermal  unit  is  the  amount  of  heat  which  passes  into  1  Ib.  of  water  when  its  temperature 
rises  1°  F.,  or  the  amount  which  passes  out  when  its  temperature  falls  1°  F.  Hence  the  number  of 
B.T.U.  produced  by  the  combustion  of  1  cu.  ft.  of  gas  is  given  by  the  product  of  the  number  of 
pounds  of  water  which  pass  through  the  calorimeter  while  1  cu.  ft.  of  gas  is  burned  and  the  rise  in 
temperature  of  the  water  in  degrees  Fahrenheit. 

Similarly,  a  calorie  is  the  amount  of  heat  which  passes  into  1  g.  of  water  when  its  temperature  rises 
1°  C.,  or  the  amount  which  passes  out  when  its  temperature  falls  1°  C. 

Since  in  1  Ib.  there  are  453.6  g.,  and  since  in  1°  F.  there  are  |°  C.,  it  follows  that  in  1  B.T.U.  there 
are  |  (453.6),  or  252,  calories.  Hence  if  the  weight  of  the  water  is  taken  in  grams  and  its  rise  in  tern 
perature  in  degrees  centigrade,  the  number  of  B.T.U.  is  given  by 

(weight  of  water  in  grams)  x  (rise  in  temperature  in  degrees  C.) 

~252~ 

[47] 


EXPERIMENT  18  (Continued) 

Question.  If  50%  of  the  heat  of  combustion  of  the  gas  burned  in  a  hot-water  heater  passes  into  the 
water,  how  much  will  it  cost  per  month  to  heat  daily  40  gal.  of  water  (1  gal.  =  8  Ib.)  from  50°  F.  to  180°  F., 
the  gas  used  being  of  the  same  quality  as  that  used  in  this  experiment,  and  the  price  being  that  charged  by 
your  home  company  ? 

RECORD  OF  EXPERIMENT 

Reading  of  water  manometer         = 

Reading  of  gas  meter  at  start       = 


number  of  cubic  feet  of  gas  used 
Reading  of  gas  meter  at  end 

Temperature  of  inflowing  water    =  ^1 

L  .•.  rise  in  temperature  of  water  = , 

Temperature  of  outflowing  water  = J 

Weight  of  pail  =  "] 

I  .•.  weight  of  water  passed  through  calorimeter  = 

Weight  of  pail  plus  water  = J 

.•.  number  of  B.T.U.  produced       =  (weight  of  water  in  pounds)  x  (rise  in  temperature  in  degrees  F.), 

,       ,      (weight  of  water  in  grams)  x  (rise  in  temperature  in  degrees  C.) 

or  number  of  B.T.U.  produced  =  i 2 s L — L^ i^ & L . 

252 

Number  of  B.T.U.  produced  per  cubic  foot  of  gas  consumed  — 

The  grade  of  gas  required  by  your  city  ordinance  is  such  that  the  number  of  B.T.U.  produced  per 
cubic  foot  of  gas  = 


[48] 


EXPERIMENT  ISA 


EFFICIENCY  AND  COST  OF  OPERATION  OF  COMMERCIAL  GAS  BURNERS 

AND  KETTLES* 

Attach  one  of  the  burners  shown  in  Fig.  37  or  any  similar  burner  to  the  improvised  gas  meter  of 
Fig.  36  or  to  an  ordinary  gas  meter. 

Place  1  or  2  qt.  (1  qt.  =  2  Ib.)  of  water  at  about  15°  C.  (59°  F.)  in  an  ordinary  teakettle. 

With  a  thermometer  take  the  temperature  of  the  water,  and  when  the  gas  meter  reads  some  tenth 
of  a  cubic  foot,  place  the  kettle 
of  water  on  the  burner  to  heat. 

Watch  the  thermometer,  and 
as  soon  as  the  water  reaches  the 
boiling  point  turn  off  the  gas 
from  the  burner  and  record  the 
reading  of  the  gas  meter. 

The  "  output,"  or  useful  heat 
obtained,  expressed  in  B.T.U., 
=  (number  of  pounds  of  water  heated)  x  (rise  in  temperature  of  water  in  degrees  Fahrenheit). 

The  "  input,"  in  B.T.U.,  =  (number  of  cubic  feet  of  gas  used)  x  (number  of  B.T.U.  produced 
by  combustion  of  1  cu.  ft.).  The  number  of  B.T.U.  produced  by  the  combustion  of  1  cu.  ft.  of  gas 
is  to  be  taken  from  Exp.  18  or  obtained  from  the  instructor. 

Questions,  a.  At  80  cents  per  thousand  cubic  feet  of  gas,  how  much  did  it  cost  to  boil  the  water  for 
this  experiment  ? 

b.  How  many  quarts  of  water  could  be  raised  from  the  same  temperature  to  the  boiling  point  for  1  cent  ? 

c.  In  a  similar  way  we  shall  later  determine  how  many  quarts  of  water  can  be  boiled  for  1  cent  when 
the  electric  heater  is  used  in  place  of  the  gas  heater.    We  can  then  see  which  is  the  more  efficient  —  in 
other  words,  the  more  economical ;  for  in  such  work  economy  is  the  real  test  of  efficiency. 


FIG.  37 


RECORD  OF  EXPERIMENT 

•.  weight  of  water 


rise  in  temperature  of  water         = 
number  of  cubic  feet  of  gas  used  = 


Weight  of  teakettle  = 

Weight  of  teakettle  +  water  = 

Initial  temperature  of  water  =  

Final  temperature  of  boiling  water  =  

First  reading  of  gas  meter  = 

Second  reading  of  gas  meter  = 

„,.,„.  , ,  JT..LI        output  in  B.T.U. 

Combined  efficiency  of  burner  and  kettle  =  — ^  „,  TT  • 

input  in  B.T.U. 

(number  of  pounds  of  water)  (rise  in  temperature  in  degrees  F.) 

~~  (number  of  cubic  feet  of  gas  used)  (number  of  B.T.U.  produced  by  1  cu.  ft.) 

*  It  is  suggested  that  this  experiment  may  be  easily  performed  at  home,  using  the  gas-range  burner  and  your  own  gas 
meter  and  kettle. 


[49] 


EXPERIMENT  19 

TO  FIND  THE  SPECIFIC  HEAT  OF  A  METAL ;  THAT  IS,  THE  'NUMBER  OF  CALORIES 
OF  HEAT  GIVEN  UP  BY  ONE  GRAM  OF  A  METAL  IN  COOLING  1°C. 

(a)  Let  three  students  work,  in  a  group  while  taking  the  data  for  this  experiment.  Let  each 
student  fill  a  boiler  like  that  of  Fig.  42  with  water  until  it  stands  about  half  an  inch  high  in  the  gauge, 
and  then  light  a  Bunsen  burner  under  each  boiler. 

(5)  Let  student  A  place  a  dipper  like  that  of  Fig.  38  on  the  left  pan  of  the  scales,  and  balance  it 
with  weights  on  the  right  pan.    Then  add  1000  g.  to  the  right  pan  and  pour  shot  into  the  dipper  until 
it  again  balances.    (Do  not  try  to  get  an  exact  balance,  one  or  two  shot,  more  or  less,  will  make  no 
appreciable  difference.)    Set  the  dipper  inside  the  boiler  and  insert  a  thermometer 
through  a  loose-fitting  cork  or  improvised  cover,  working  it  well  down  into  the  shot. 

(c)  Let  student  B  follow  the  instructions  in  (5),  using  300  g.  of  iron  pellets 
(or  nails),  and  student  C,  using  150  g.  of  aluminum  pellets  (or  aluminum  punchbags). 

(d*)  Each  student  should  now  weigh  or  measure  out  250  g.  of  cold  water  (12°  C. 
or  15°  C.  below  room  temperature)  and  place  it  in  the  inner  vessel,  which  is  sup- 
ported by  its  ring  in  the  outer  vessel  of  the  calorimeter. 

(ji)  With  a  glass  rod  or  pencil  stir  the  metals  every  four  or  five  minutes  until  Fl<>-  38 

their  temperatures  become  about  95°  C.  to  100°  C. 

(/)  Let  each  student  now  read  the  temperature,  on  the  same  thermometer,  of  the  cold  water  pre- 
pared by  A,  when  it  is  about  9°  C.  or  10°  C.  below  room  temperature,  see  that  all  dew  on  the  inner 
calorimeter,  if  any  formed,  is  wiped  off,  record  the  temperature  ot  the  cold  water  and  that  of  the  shot, 
estimating  tenths  of  a  degree,  and  quickly  pour  the  lead  shot  from  the  dipper  into  his  calorimeter. 
Stir  the  mixture  two  minutes  and  record  the  temperature  of  the  mixture,  carefully  estimating  tenths 
of  a  degree. 

(<7)  In  the  same  way  as  in  (/)  the  three  students  should  take  the  data  with  the  materials  prepared 
by  B  and  C,  in  each  of  these  cases  as  before  having  the  cold  water  9°  C.  or  10°  C.  below  room  tempera- 
ture just  before  pouring  the  hot  metal  into  the  calorimeter.  Now  spread  out  the  metals  used  on 
cloths  to  dry. 

(A)  If  we  let  Sm  represent  the  number  of  calories  of  heat  given  up  by  1  g.  of  metal  in  cooling 
1°  C.,  that  is,  its  specific  heat,  then  in  cooling  from  the  temperature  of  the  metal,  £m,  to  the  tempera- 
ture of  the  mixture,  ?mix,  1  g.  of  the  metal  would  give  up  (tm  —  tmix)  Sm  calories ;  and  the  total  mass  of 
the  metal,  JfTO,  would  give  up  Mm  (tm  —  t  mix)  Sm  calories.  This  must  equal  the  heat  received  by  the 
water  and  calorimeter  according  to  the  law  of  mixtures.  (Heat  lost  by  the  body  or  bodies  cooled  = 
heat  gained  by  the  body  or  bodies  warmed.) 

We  nave  Calories  out  of  Metal  Calories  into  Water  Calories  into  Calorimeter* 


JC  O,  -  *.i*)  ^m  =  M*  On*  -<„)!  +  Mc  (t^  -  Q  .095, 

where  the  subscript  m  refers  to  the  metal  used,  "  mix  "  to  mixture,  c  to  calorimeter,  and  w  to  water  alone. 

(f)  Write  out  the  numerical  equation  for  each  metal  used  and  solve  it  for  Sm.  Explain  what  each 
part  of  the  equation  represents. 

State  in  your  notebook  what  you  understand  to  be  represented  by  the  quantity  Sm  which  you 
have  found,  t 

*  Take  the  specific  heat  of  the  calorimeter  as  .095. 

t  A  further  very  interesting  experiment  which  may  be  inserted  for  the  benefit  of  those  who  have  time  and  inclination  for 
extra  work  is  the  following : 

To  find  the  temperature  of  a  white-hot  body.  By  means  of  a  thin  copper  wire  suspend  from  a  support  placed  from  50  cm.  to 

[51] 


EXPERIMENT  19    (Continued) 

When  the  shot  and  the  water  were  mixed,  the  changes  in  the  temperature  of  each  took  place  very 
rapidly  at  first,  but  very  slowly  as  the  temperature  of  each  approached  the  final  value.  Can  you  see 
a  reason,  therefore,  why  it  was  advisable  to  choose  the  conditions  so  that  the  final  temperature  should 
be  close  to  the  temperature  of  the  room  ?  Remember  in  your  answer  that  it  was  necessary  to  wait  two 
or  three  minutes  for  the  mixture  to  reach  its  final  temperature,  and  that  a  body  which  is  hotter  than 
the  room  is  always  losing  heat  to  the  room,  while  one  which  is  colder  than  the  room  is  always  gaining 
heat  from  it.  It  is  these  losses  of  heat  by  radiation  which  constitute  the  greatest  difficulty  in  the  way 
of  accurate  measurements  by  the  method  of  mixtures. 

RECORD  OF  EXPERIMENT 


METAL 

WEIGHT  OF 

METAL 

Mm 

TEMPERA- 
TURE OF 
METAL 
tm 

WEIGHT  OF 
WATER 
Mm 

TEMPERA- 
TURE OF 
WATER 

(. 

TEMPERA- 
TURE OF 
MIXTURE 

tmil 

WEIGHT 
OF  CALO- 
RIMETER 
Mc 

EXPERI- 
MENTAL 
VALUE  OF 

Sm 

ACCEPTED 
VALUE  OF 

Sm 

PER  CENT 
OF  ERROR 

Lead 

Iron 

Aluminum 

Equation  for  lead : 
Equation  for  iron : 
Equation  for  aluminum : 

100  cm.  above  the  table  a  piece  of  copper  rod  about  2  cm.  long  and  12  mm.  in  diameter.  Adjust  the  length  of  the  suspension 
BO  that  the  copper  hangs  in  the  hottest  part  of  a  Bunsen  flame  (just  above  the  inner  cone). 

Weigh  a  calorimeter  of  300  cc.  capacity ;  then  fill  it  about  half  full  of  water  whose  temperature  has  been  reduced  12°  C.  or 
16°  C.  below  that  of  the  room,  and  weigh  again.  Then  replace  it  in  its  jacket. 

After  the  copper  has  been  heating  for  about  ten  minutes  take  the  temperature  of  the  water  veiy  carefully  (it  should  now 
be  from  8°  to  10°  below  the  temperature  of  the  room) ;  then,  all  in  the  same  second,  remove  the  flame  and  lift  the  calorimeter 
so  as  to  bring  the  white-hot  copper  to  the  bottom  of  the  vessel  of  water. 

Stir  the  water  thoroughly  for  one  or  two  minutes  ;  then  take  the  final  temperature. 

Weigh  the  copper  rod  and  with  it  as  much  of  the  copper  wire  as  was  immersed. 

Assuming  that  0.95  calories  (the  specific  heat  of  copper)  came  out  of  each  gram  of  copper  for  each  degree  of  fall  in  its 
temperature,  calculate  what  was  the  temperature  of  the  white-hot  copper. 

Duplicate  conditions  as  nearly  as  possible  and  see  how  closely  two  observations  will  agree. 


[52] 


EXPERIMENT  20 


FIG.  39 


THE  MECHANICAL  EQUIVALENT  OF  HEAT 

The  object  of  this  experiment  is  to  show  that  when  a  falling  body  strikes  the  earth,  the  kinetic 
energy  of  the  moving  mass  is  transformed  into  the  energy  of  molecular  vibrations,  that  is,  into  heat, 
and  to  find  how  many  gram  meters  of  mechanical  energy  must  disappear  in  order  to  produce  1  calorie 
of  heat.  This  quantity  is  called  the  mechanical  equivalent  of  heat. 
It  is  obtained  by  finding  the  rise  in  the  temperature  of  shot  when  it 
falls  through  a  known  height. 

Pour  about  2  kg.  of  dry  shot  into  a  metal  vessel  and  set  it  in  a 
cool  place,  for  example,  in  a  bath  of  ice  water,  until  its  temperature 
is  5°  C.  or  6°  C.  below  that  of  the  room. 

Pour  this  shot  into  a  paper  tube  (Fig.  39)  about  a  meter  long 
and  5  or  6  cm.  in  diameter,  made  by  rolling  up  a  large  number  of 
turns  of  heavy  brown  paper  and  then  securing  them  with  glue  and 
string.  The  tube  should  be  closed  with  two  tightly  fitting  corks. 

Mix  the  shot  very  thoroughly  by  shaking  the  tube  and  by  slowly 
inclining  it  so  that  the  shot  will  run  from  end  to  end.  In  so  doing, 
however,  grasp  the  tube  near  the  middle  rather  than  at  the  ends, 
for  it  is  desirable  that  the  temperature  of  the  ends  be  not  influenced  by  the  heat  of  the  hands* 

After  inverting  the  tube  in  this  way  from  five  to  ten  times,  remove  the  upper  cork  A  and  insert 
cork  C  (Fig.  39),  through  which  passes  a  thermometer ;  then  gradually  incline  the  tube  until  all  the 
shot  has  run  down  to  the  thermometer  end  and  there  completely  surrounds  the  bulb. 

Holding  the  tube  inclined  as  in  the  figure,  twist  the  thermometer  around  in  the  shot  for  about  two 
minutes  and  then  take  the  temperature.  If  this  is  more  than  2°  C.  or  3°  C.  below  the  temperature  of  the 
room,  continue  the  shaking  and  rolling  of  the  shot  from  one  end  to  the  other  until  its  temperature  has 
risen  to  within  about  3°  C.  of  that  of  the  room. 

Record  this  temperature,  quickly  replace  cork  C  by  cork  A,  hold  the  tube  upright,  as  in  the  figure, 
and  turn  it  end  for  end,  say,  seventy  times  in  rapid  succession,  placing  the  lower  end  on  the  table 
at  each  reversal,  so  that  the  falling  shot  may  not  force  out  the  corks.  At  each  reversal  the  potential 
energy  acquired  by  the  shot  in  being  lifted  the  length  of  the  tube  is  converted  into  kinetic  energy 
in  the  descent,  and  this  kinetic  energy  is  all  transformed  into  heat  energy  at  the  bottom.  On  account 
of  the  poor  conductivity  of  cork  and  paper  practically  all  of  this  heat  goes  into  the  shot  and  but  an 
insignificant  portion  of  it  into  the  corks  and  the  tube. 

After  the  seventy  reversals  very  quickly  replace  cork  A  by  cork  C  and  take  as  before  the  final 
temperature  of  the  shot. 

Remove  cork  (7,  set  the  tube  on  end,  and  measure  the  distance  from  the  top  of  the  shot  to  the 
position  which  was  occupied  by  the  bottom  of  cork  A.  This  is  the  mean  height  through  which  the 
shot  has  fallen  at  each  reversal. 

The  total  number  of  gram  meters  of  work  which  have  been  transformed  into  heat  is  the  weight 
W  of  the  shot  X  the  height  h  of  fall  (expressed  in  meters)  X  70.  The  number  of  calories  of  heat 
developed  is  the  weight  of  the  shot  W  x  its  specific  heat  (.0315)  X  the  rise  in  temperature  (tz  —  t^). 
Hence,  if  J  represents  the  number  of  gram  meters  of  energy  in  a  calorie,  we  have 

J-  Wx  («2-Q  X. 0315  =  70  •  W-  h. 
70  h 


T53] 


EXPERIMENT  20   (Continued) 

It  will  be  noticed  that  the  weight  W  of  the  shot  cancels  out ;  hence  it  need  not  be  taken. 

In  the  above  directions  the  attempt  is  made  to  eliminate  radiation  and  conduction  losses  by  mak- 
ing the  initial  temperature  of  the  shot  about  as  far  below  the  temperature  of  the  room  as  the  final 
temperature  is  to  be  above  it.  This  is  the  usual  way  of  eliminating  radiation,  when,  as  in  this  case, 
the  change  in  temperature  between  the  readings  of  the  initial  and  final  temperatures  takes  place  rapidly 
and  at  a  uniform  rate. 

Repeat  the  experiment  several  times  if  time  permits. 

What  conclusions  do  you  draw  from  your  experiment  ? 

The  chief  source  of  error  in  the  experiment  arises  from  the  fact  that  the  thermometer  requires 
considerable  time  to  come  to  the  temperature  of  the  shot.  During  all  this  time  the  shot  is  gaining  or 
losing  heat  by  conduction  and  radiation,  so  the  temperature  indicated  may  not  be  quite  the  mean 
temperature  of  the  shot.  This  source  of  error  is  unavoidable. 

Questions,  a.  Why  did  we  attempt  to  have  the  initial  temperature  as  far  below  the  temperature  of  the 
room  as  the  final  temperature  was  above  it  ? 

6.  If  iron  shot  had  been  used  instead  of  lead  shot,  would  the  rise  in  temperature  be  more  or  less  than  it 
was  with  lead  shot  ? 

c.  Why  is  lead  better  for  this  experiment  than  any  of  the  other  metals  ? 

RECORD  OF  EXPERIMENT 

Illustrative  data  taken  by  a  student. 

First  Trial  Second  Trial  Third  Trial 

Temperature  of  room    =    18.5°  C.  18.5°  C.  18.5°  C.             Mean  value  =  437  g.  m. 

Initial  temperature        =    16.0°  C.  17.1°  C.  16.7°  C. 

Final  temperature          =    21.7°  C.  22.6°  C.  21.0°  C.             Accepted  value  =  427  g.  m. 

Number  of  reversals      =  100  100  80                                                                      % 

Height  of  fall  (A)           =        .76  m.  .76  m.                 .76  m. 

Mechanical  equivalent  =  423  g.  m.  439  g.  m.  449  g.  m.           Per  cent  of  error  =  2.4. 

NOTE.  The  error  in  this  experiment,  even  with  careful  work,  may  sometimes  be  as  high  as  10%. 


EXPERIMENT  21 
COOLING  THROUGH  CHANGE  OF  STATE 

I.  Solidification  a  heat-evolving  process.  The  object  of  this  experiment  is  to  show  that  just  as  it 
requires  an  expenditure  of  heat  energy  to  melt  ice  or  any  other  crystalline  substance,  so  when  water  or  any 
liquid  freezes,  that  is,  changes  back  to  the  crystalline  form,  heat  energy  is  given  up  to  the  surroundings. 

Support  vertically  in  a  burette  holder  or  other  clamp  a  test  tube  in  which  enough  loose  crystals  of 
acetamide  have  been  placed  to  fill  it  about  a  third  full.  Then  heat  gently  with  a  Bunsen  burner  until 
the  crystals  are  all  melted.*  Slowly  insert  a  thermometer  into  the  liquid,  but  watch  the  thread  all 
the  time,  and  if  it  rises  to  within  half  an  inch  of  the  top  of  the  bore,  instantly  remove  the  bulb  from 
the  liquid.  The  thermometer  will  burst  under  the  force  of  expansion  of  the  mercury  if  the  thread  reaches 
the  top  of  the  bore.  If  there  is  an  expansion  chamber  at  the  top,  this  danger  is  of  course  avoided.  If 
there  is  no  expansion  chamber,  it  will  be  safer  to  melt  the  acetamide  by  dipping  the  tube  into  boiling 
water  rather  than  by  applying  the  flame  directly. 

As  soon  as  the  liquid  acetamide  has  cooled  down  to  about  100°  C.,  insert  the  thermometer  in  it 
permanently  and,  without  touching  further  either  the  tube  or  the  thermometer,  watch  carefully  both 
the  liquid  and  the  thread  of  mercury 
as  cooling  takes  place.  The  tempera- 
ture may  fall  as  low  as  60°  C.  before 
crystallization  begins.  As  soon  as 
crystals  begin  to  form,  what  sort 
of  a  temperature  change  do  you 
observe  ?  What  conclusion  do  you 
draw  from  this  observation  ?  Watch 
the  temperature  for  two  or  three 
minutes  more  and  decide  whether  or 


not  the  temperature  of  a  solidifying 
liquid  remains  constant  during  the 
process  of  solidification.  Since  it  is 
giving  up  heat  rapidly  all  this  time, 
it  must  get  it  from  some  source. 
What  must  this  source  be  ? 

II.  The  curve  of  cooling.  Again 
raise  the  temperature  to  100°C.,  taking  the  precautions  mentioned  above  against  breaking  the  thermome- 
ter. Record  the  temperature  every  half  minute  as  the  substance  cools  from  about  100°  C.  to  45°  C. 
Plot  these  observations  in  the  manner  shown  in  Fig.  40,  temperatures  being  represented  by  vertical 
distances  and  times  by  horizontal  distances.  Thus,  the  observations  plotted  in  the  figure  began  at 
11 : 15  A.M.  and  continued  to  11 :  45  A.M.  The  curve  shows  that  between  11 : 15  and  11 : 19.5  the 
temperature  fell  rapidly  from  100°  C.  to  71.8°  C.,  that  it  then  rose  suddenly  to  79°  C.,  remained  there 
five  minutes,  and  then  fell  slowly  during  the  next  twenty  minutes  from  79°  C.  to  43.5°  C. 

Write  in  your  notebook  a  similar  explanation  of  your  own  curve.  Almost  any  substance,  if  kept 
very  quiet  and  cooled  through  its  freezing  point,  will  show  the  phenomenon  of  undercooling  exhibited 
here  by  the  acetamide ;  that  is,  its  temperature  will  fall  a  little  below  the  freezing  point  before 
crystallization  gets  started.  It  will  then  rise  suddenly  to  the  freezing  point  and  remain  there  until 
crystallization  is  practically  complete.  Why  ? 


ins 


*  If  the  acetamide  has  absorbed  much  moisture,  boil  it. 
[55] 


EXPERIMENT  21    (Continued) 

If  time  permits,  dip  a  test  tube  containing  a  little  distilled  water  into  a  freezing  mixture  of  salt 
water  and  ice,  the  temperature  of  which  is,  say,  —  8°  C.,  and  see  if  water  too  will  not  show  the  same 
behavior.  (The  tube  must  be  kept  very  quiet.)  If  you  get  the  temperature  down  to  —  2°  C.  or  —  3°  C., 
lift  the  test  tube,  stir,  and  observe  the  instant  formation  of  the  crystals  of  ice.  If  you  wish  to  try  a 
substance  which  does  not  undercool,  treat  a  little  naphthaline  *  precisely  as  you  treated  the  acetamida 

RECORD  OF  EXPERIMENT 


TIME 

TEMPERATURE 

Hour 

Minute 

etc. 

etc. 

etc. 

»  Naphthaline  can  be  obtained  at  any  drug  store.  Acetamide  will  have  to  be  purchased  at  a  chemical  supply  house. 


[56] 


EXPERIMENT  22 
THE  HEAT  OF  FUSION  OF  ICE 

The  heat  of  fusion  of  ice,  that  is,  the  number  of  calories  of  heat  required  to  change  a  gram  of  ice 
at  0°  C.  into  water  at  0°  C.,  or  the  number  given  up  when  a  gram  of  water  changes  to  ice,  may  be 
determined  experimentally  as  follows : 

Weigh  the  inner  vessel  of  a  calorimeter  of  about  300  cc.  capacity,  first  when  empty  and  then  after 
it  has  been  filled  about  two-thirds  full  of  water.* 

Heat  this  water  to  a  temperature  of  about  25°  C.  above  that  of  the  room ;  then  support  the  inner 
vessel  by  its  ring  in  the  outer  vessel  of  the  calorimeter. 

Prepare  a  lump  of  clear  ice  of  about  the  size  of  a  hen's  egg  and  perform  the  following  operations 
in  quick  succession : 

While  one  student  is  drying  the  ice  upon  a  towel,  let  another  stir  the  water  in  the  calorimeter 
thoroughly.  If  its  temperature  is  less  than  15°  C.  above  that  of  the  room,  heat  it  up  again  until  it  is 
between  15°  C.  and  25°  C.  above.  Again  check  the  weight,  for  the  loss  by  evaporation  may  not  have 
been  inappreciable.  Stir  vigorously ;  then  quickly  take  a  careful  reading  of  the  temperature,  keeping 
the  thermometer  bulb  all  the  time  immersed,  and  not  more  than  a  second  or  two  after  the  reading  let 
the  first  student  drop  the  dry  ice  into  the  water,  being  very  careful  not  to  spill  a  drop.  The  splash 
may  often  be  avoided  by  letting  the  ice  slide  along  the  thermometer  into  the  water. 

Stir  continuously  while  the  ice  is  melting  and  read  the  temperature  of  the  water  just  after  the  ice 
has  all  disappeared.  This  temperature  should  be  from  2°  C.  to  10°  C.  below  the  temperature  of  the 
room.  If  it  should  happen  to  be  above  the  room  temperature,  try  again  with  a  slightly  larger  piece  of 
ice.  The  limits  here  given  are  chosen  so  as  to  make  it  legitimate  to  assume  that  the  heat  exchanges 
which  take  place  between  the  calorimeter  and  the  room  are,  on  the  whole,  negligible. 

Again  weigh  the  inner  vessel  of  the  calorimeter,  with  its  contained  water,  and  take  the  difference 
between  this  weighing  and  the  last  as  the  weight  of  the  ice. 

Let  x  represent  the  heat  of  fusion  of  ice  and  w  the  weight  in  grams  of  the  ice  melted.  Then  the 
number  of  calories  expended  in  melting  the  ice  is  wx.  After  the  ice  is  melted  it  becomes  w  grams  of 
water  at  0°  C.  This  water  is  then  raised  to  the  final  temperature  t  of  the  mixture.  The  number  of 
calories  required  for  this  operation  is  wt.  All  of  this  heat  has  come  from  the  cooling  of  the  water  and 
the  calorimeter.  If  the  weight  of  the  water  cooled  is  W  and  its  initial  temperature  ^,  while  the  water 
equivalent  of  the  calorimeter  is  e,  (.095  x  weight  of  calorimeter),  then  the  total  number  of  calories 
given  up  by  the  water  and  calorimeter  is  (W  +  e)  (^  —  t).  Hence,  by  equating  " heat  lost "  and 
"  heat  gained,"  we  have  the  equation  (  W+  e)  (^  —  f)  =  wx  +  wt,  from  which  compute  x. 

Questions,    a.  What  is  meant  by  "  latent  heat  of  ice,"  the  quantity  which  you  found  above  ? 

b.  Explain  why  ice  rather  than  ice  water  is  used  to  cool  lemonade. 

c.  Explain  what  each  part  of  your  numerical  equation  represents. t 

*  If  you  use  the  small  cylinders  of  Exp.  3  for  the  calorimeters,  take  just  half  of  the  amounts  of  ice  and  water  indicated. 

t  A  further  experiment  on  latent  heat,  which  may  be  introduced  for  the  benefit  of  those  who  have  time  and  inclination 
for  extra  work,  is  the  following : 

To  find  the  heat  of  condensation  of  steam.  Pass  dry  steam  into,  say,  250  g.  of  cold  water,  the  temperature  of  which  is  10°  C. 
below  that  of  the  room,  until  the  temperature  is  10°  above  that  of  the  room.  Weigh  again  to  find  the  weight  w  of  the  steam 
condensed. 

Let  x  represent  the  heat  of  condensation  of  steam,  that  is,  the  number  of  calories  of  heat  given  up  by  a  gram  of  steam  in 
changing  from  steam  to  water  at  the  same  temperature.  Then  the  number  of  calories  of  heat  produced  by  the  condensation 
of  the  steam  is  wx.  The  water  formed  by  the  condensation  of  the  steam  in  cooling  to  the  final  temperature  t  of  the  mixture 
will  give  up  w  (100  —  t)  calories.  If  the  weight  of  the  water  heated  is  W  and  its  initial  temperature  ^ ,  while  the  water 
equivalent  of  the  calorimeter  is  e,  then  the  heat  exchanges  are  given  by  the  equation 

wx  +  w  (100  -  t)  =  (W  +  e)  (t  -  tj. 
[57] 


EXPERIMENT  22   (Continued) 

RECORD  OF  EXPERIMENT 

Weight  of  calorimeter  = 

Weight  of  calorimeter  +  water  =  

.-.  weight  of  water  =  

Temperature  of  room  = 

Initial  temperature  of  water  = 

Final  temperature  of  water  = 

.-.  fall  in  temperature  of  water  = 

Weight  of  calorimeter  +  water  +  ice  = 

.•.  weight  of  ice  = 

Equation 

.-.  heat  of  fusion  of  ice,  x,  = caL 

Accepted  value  is  80. 

.•.  per  cent  of  error  = 


[58] 


EXPERIMENT  23 
THE  BOILING  POINT  OF  ALCOHOL 

The  boiling  point  of  a  liquid  is  denned  as  the  temperature  at  which  the  pressure  of  its  saturated 
vapor  becomes  equal  to  the  atmospheric  pressure.  There  are,  therefore,  two  ways  in  which  the  boiling 
point  of  alcohol  may  be  obtained,  and  these  two  ways  should  give  identical  results.  The  first  is  to 
confine  the  liquid  and  its  vapor  alone  in  a  closed  vessel,  and  then  to  measure  the  pressure  exerted  by 
the  vapor  at  different  temperatures.  That  temperature  at  which  the  pressure  becomes  equal  to  atmos- 
pheric pressure  will  then  be  the  boiling  temperature.  The  second  and  more  direct  way  consists  in 
simply  boiling  the  liquid  in  an  open  vessel  and  observing  the  temperature  indicated  by  a  thermometer 
held  in  the  vapor  rising  from  the  liquid. 

I.  Temperature  at  which  pressure  of  saturated  vapor  becomes  equal  to  atmospheric  pressure.  A  glass 
tube  A  (Fig.  41)  is  closed  at  one  end,  and  is  then  bent  into  the  U-shape  and  partially  filled  with  mer- 
cury. Some  alcohol  is  then  poured  in,  which  by  careful  tilting  is  worked  around  into  the  closed  arm, 
while  the  air  is  altogether  worked  out  of  this  arm.  With  this  arrangement  proceed  as  follows : 

Immerse  the  tube  and  a  thermometer  together  in  a  vessel  of  water,  and,  keeping  the  short 
arm  completely  immersed,  heat  slowly,  with  constant  stirring.  As  the  temperature  increases  a 
point  is  reached  at  which  alcohol  vapor  begins  to  form  in  the  closed  tube.  Still  further 
increase  in  temperature  causes  the  mercury  to  sink  farther  and  farther  in  the  closed  end. 
When  the  levels  of  the  mercury  in  the  two  arms  are  the  same,  it  is  clear  that  the  pressure  of 
the  alcohol  vapor  is  just  equal  to  the  atmospheric  pressure.  Raise  the  temperature  of  the 
water  gradually  and  stir  thoroughly  until  this  condition  is  reached ;  then  read  and  record  yIQ>  41 
the  temperature. 

Continue  heating  until  the  level  in  the  short  arm  is  5  cm.  lower  than  that  in  the  long  one.  Then 
again  read  the  thermometer  and  compute  how  much  the  boiling  point  of  alcohol  increases  per  centi- 
meter increase  in  the  barometric  pressure. 

•    II.  Temperature  of  vapor  rising  from  boiling  liquid.   Place  a  little  alcohol  in  a  large  test  tube ;  put 
few  tacks  in  the  bottom  of  the  tube  in  order  to  insure  smooth  boiling ;  then  immerse  the  lower  end 
of  the  tube  in  a  vessel  of  water  and  heat  the  water  until  the  alcohol  boils  vigorously.    Hold  the  bulb 
of  a  thermometer  in  the  tube  a  little  distance  above  the  surface  of  the  boiling  liquid.    As  soon  as  the 
thermometer  reading  becomes  stationary,  take  the  temperature  and  compare  with  that  obtained  in  I. 

Questions,  a.  If  the  test  tube  of  alcohol  were  placed  under  the  receiver  of  an  air  pump,  how  would  its 
boiling  point  change  as  the  air  was  exhausted  from  the  receiver  ? 

6.  If  the  boiling  point  of  alcohol  was  determined  in  a  deep  mine,  would  it  be  higher  or  lower  than  you 
found  it  to  be  in  I,  (#)  or  II,  (a).  (See  data  record.) 

RECORD  OF  EXPERIMENT 
I.  (a)  Barometer  reading  = cm. 

(6)  Temperature  at  which  alcohol  vapor  exerts  a  pressure  equal  to  the  atmospheric  pressure  = °  C. 

(c)  Temperature  at  which  alcohol  vapor  exerts  a  pressure  equal  to  the  atmospheric  pres- 
sure +  5  cm.  of  mercury  = °C. 

(rf)  Rise  in  boiling  point  of  alcohol  per  centimeter  increase  in  pressure  = °C. 

(e)  Boiling  point  of  alcohol  at  76  cm.  pressure  = °  C. 

II.  (a)  Temperature  of  vapor  rising  from  boiling  alcohol  = °G. 

Difference  between  results  of  I, '(6)  and  II,  (a)  = °C. 

[59] 


EXPERIMENT  24 

TO  TEST  THE  FIXED  POINTS  OF  A  THERMOMETER,  AND  TO  FIND  THE  CHANGE 
IN  THE  BOILING  POINT  OF  WATER  PER  CENTIMETER  CHANGE  IN  THE 

BAROMETRIC  PRESSURE 

Fill  the  boiler  of  Fig.  42  half  full  of  water  and  thrust  the  thermometer  through  a  tightly  fitting 
cork  in  the  top  until  the  100°  point  is  only  2  or  3  mm.  above  the  cork. 

Attach  an  open-arm  manometer  u  (Fig.  42)  to  the  exit  0,  and  then  boil,  regulating  the  flame  until 
the  mercury  stands  at  the  same  height  in  both  arms  of  the  manometer. 

After  the  water  has  been  boiling  steadily  for  two  or  three  minutes,  read  the  thermometer  very 
carefully.  Then  take  the  barometer  reading.  Next  place  a  piece  of  tightly  fitting  rubber  tubing  over 
the  escape  tube  e  and  partly  close  the  free  end  of  it  with  a  pinchcock  until  the  difference  in  the  levels 
in  the  manometer  arms,  due  to  the  partial  closing  of  the  vent  for  the  steam, 
amounts  to  2  or  3  cm.  Read  the  thermometer  and,  with  a  meter  stick,  the 
difference  in  the  levels  in  the  manometer  arms. 

Close  the  pinchcock  still  further,  until  the  difference  in  level  amounts  to  4  or 
5  cm. ;  then  read  again. 

Continue  thus,  taking  readings  at  intervals  of  about  3  cm.,  until  the  differ- 
ence in  level  amounts  to  9  or  10  cm.  It  may  be  necessary  to  use  several  burners 
in  order  to  obtain  the  last  readings,  for  the  steam  must  be  generated  very  rapidly  in 
order  to  compensate  for  the  inevitable  leakage. 

From  each  of  these  readings  calculate  the  changes  produced  in  the  boiling  point 
by  a  change  of  1  cm.  in  the  barometric  height.  Take  a  mean  of  all  these  calculations 
as  the  correct  value  of  this  quantity. 

From  this  result  and  the  barometer  reading  calculate  what  your  thermometer 
would  read  under  a  pressure  of  76  cm.  The  error  in  the  graduation  of  the  ther- 
mometer is  the  difference  between  this  result  and  100. 

Test  the  zero  point  of  the  same  thermometer  by  sinking  it  up  to  the  zero  mark  in  a  funnel  filled 
with  melting  snow,  or  with  finely  chopped  ice  over  which  a  little  water  has  been  poured,  and  allowing 
it  to  remain  there  until  the  thread  is  stationary. 

Questions,  a.  Why  will  a  thermometer  placed  in  a  steam  boiler  often  register  as  high  a  temperature 
as  150°  C.  ? 

b.  When  a  steam  boiler  bursts,  the  pressure  to  which  the  steam  and  water  was  subjected  almost  instantly 
changes  to  what  pressure  ? 

c.  How  do  you  account  for  the  production  of  a  very  much  larger  quantity  of  steam  when  a  boiler 
explodes  than  was  in  the  boiler  just  before  the  explosion  ? 


FIG.  42 


RECORD  OF  EXPERIMENT 

Trial  1  Trial  2 


Trial  3  Trial  4 

Difference  in  levels  in  gauge  =  cm cm cm 

Corresponding  boiling-point  readings  = ° C °C °C 

Change  in  boiling  point  per  cm.  = °C °C °C 

Mean  change  per  cm.  = °C.         Barometer  height  = cm. 

Boiling  point  at  76  cm.  = °C.         Error  .°C. 

Freezing  point  (reading  on  thermometer)    = °  C.         Error  = °C. 

[61] 


FIG.  43 


EXPERIMENT  25 
MAGNETIC  FIELDS* 

I.  The  magnetic  field  about  a  bar  magnet,  (a)  Lay  a  bar  magnet  in  the  groove  of  the  board 
shown  in  (Fig.  43, 1).  Pin  a  sheet  of  blue-print  paper  over  the  magnet ;  from  a  sifter  containing  iron 
filings  sift  the  filings  evenly,  but 
not  too  thickly,  over  the  paper 
from  a  height  of  a  foot  or  two. 
Tap  the  paper  gently  with  a  pencil. 
The  filings  will  be  found  to  have 
arranged  themselves  in  lines  run- 
ning in  symmetrical  curves  from 
one  pole  around  to  the  other. 


(5)  Hold  a  short  compass 
needle  in  a  number  of  positions 
over  the  board,  and  observe 
whether  or  not  there  is  any  connection  between  the  direction  of  the  curved  lines  and  the  direction 
taken  by  the  needle.  These  lines  simply  indicate  the  direction  of  the  magnetic  force.  They  are  called 
magnetic  lines  of  force.  With  a  lead  pencil  indicate  on  the  paper  the  N  and  S  poles  of  the  magnet. 

(<?)  Carefully  place  the  board  in  strong  sunlight  without  jarring  the  filings,  and  wait  until  the 
uncovered  parts  of  the  paper  have  turned  pale  blue.  Return  the  filings  to  the  box  and  put  the  blue- 
print paper  to  soak  in  water  for  about  five  minutes.  Place  the  paper  flat  against  a  pane  of  glass  to 
dry,  and  when  it  is  dry  fasten  it  in  your  notebook. 

If  blue-print  paper  is  not  provided,  or  if  the  sun  is  not  bright  enough  to  make  satisfactory  prints, 
simply  draw  in  your  notebook  a  copy  of  the  curves  shown  by  the  filings.  In  these  drawings,  as  on 
the  blue  prints,  indicate  the  N  and  S  poles  of  the  magnets  and  furnish  the  lines  with  arrows  pointing 
in  the  direction  in  which  an  N  pole  tends  to  move.  (An  N  pole  is  one  which,  when  the  magnet  is 
freely  suspended,  points  toward 
the  north.) 

II.  The  magnetic  field  about  cer- 
tain combinations  of  horseshoe  mag- 
nets. Using  the  reverse  side  of 
the  board  used  in  I  and  the  horseshoe  magnets  of  the  improvised  D'Arsonval  galvanometer  of  Exp.  30, 
make  blue  prints  or  drawings  of  each  of  the  illustrations  in  Fig.  44.  Be  sure  to  mark  the  location  of 
the  N  and  S  poles  on  each  blue  print  or  drawing.  In  2,  place  the  bar  of  soft  iron  about  1  in.  from  the 
end  of  the  magnet.  In  3  and  4,  place  the  ends  of  the  magnets  about  2  or  3  in.  apart. 


Questions,    a.  Does  each  iron  filing  become  a  magnet  ?   How  do  you  know  ? 

b.  Why  do  the  filings  point  along  the  lines  of  force  ? 

c.  What  is  a  line  of  force  ? 

d.  What  is  the  nature  of  the  lines  of  force  between  two  attracting  poles  ?  between  two  repelling  poles  ? 
«.  What  property  of  iron  does  Fig.  44,  2,  show  ? 

»  To  make  boards  for  this  experiment  make  upper  pieces  of  Fig.  43,  1,  of  same  thickness  as  bar  magnets  and  separate 
them  by  the  width  of  the  magnet.  For  the  lower  pieces  of  Fig.  43,  1  (upper  of  Fig.  43,  2),  use  pieces  of  same  thickness  as 
horseshoe  magnets  and  separate  them  by  the  width  of  the  horseshoe  magnet.  A  notch  cut  into  these  pieces  receives  the  soft 
iron  of  Fig.  44,  2. 


[63] 


I.  Making  a  permanent  magnet.    Mark  one  end  of  a  knitting  needle  with  a  file  for  the  sake  of 
identification. 

(a)  Stroke  it  once  from  end  to  end  with  the  .2V  pole  of  a  horseshoe  or  bar  magnet.  Place  the  needle 
on  the  table  in  the  east-and-west  line  which  passes  through  the  middle  of  a  compass  needle  resting 
upon  the  table,  and  slide  the  knitting  needle  up  toward  the  compass  until  it  produces  in  it  a  deflection 
of  10° ;  then  mark  the  positions  of  the  two  ends  of  the  knitting  needle  on  the  table.  Does  the  near 
end  of  the  knitting  needle  repel  or  attract  the  north-seeking  end  of  the  compass  needle  ?  Is  it  an  N  or 
an  S  pole  ?  (If  in  doubt,  suspend'  the  needle  in  the  middle  by  a  thread  and  a  wire  stirrup  and  see 
which  end  points  north.) 

(6)  Reverse  the  knitting  needle  so  that  the  second  end  occupies  exactly  the  position  originally 
occupied  by  the  first.  Compare  the  strengths  and  signs  of  the  two  poles. 

(<?)  Stroke  the  needle  once  more  with  the  magnet  precisely  as  at  first,  and  again  bring  it  to  pre- 
cisely the  same  position.  Is  the  deflection  increased  ?  How  much  ? 

(d)  Continue  to  stroke  the  magnet  in  the  same  way  until  it  is  saturated,  that  is,  until  further 
stroking  produces  no  more  change  in  the  effect  upon  the  compass. 

II.  Effect  of  jars  on  a  saturated  magnet,    (a)  Drop  the  needle  on  the  floor  and  again  test  its 
strength  exactly  as  before.    Record  the  change. 

(6)  Strike  the  needle  a  number  of  sharp  blows  against  the  table  and  test  again. 
(<?)  If  magnetization  consists  in  a  particular  arrangement  of  the  molecules  of  the  needle,  what 
effect  would  you  expect  violent  jars  like  the  above  to  have  upon  it  ? 

III.  Effect  of  breaking  a  magnetized  needle,    (a)  Magnetize  a  long  darning  needle  and  note  which 
end  is  N  and  which  S.    Then  dip  the  whole  needle  into  a  box  of  iron  filings  and  note  whether  or  not 
it  possesses  any  appreciable  magnetism  in  the  middle. 

(6)  Break  it  in  two  and  test  the  two  freshly  broken  ends  first  by  means  of  the  compass  and  then 

«  means  of  the  iron  filings.    Test  also  the  old  ends, 
(c)  Break  one  of  the  halves  again  if  possible  and  repeat  as.  above. 

(dT)  Summarize  the  results  of  these  experiments  and  explain  the  observed  effects  on  the  assump- 
tion that  a  magnet  consists  of  rows  of  molecular  magnets  arranged  end  to  end. 

IV.  Effects  of  heating  a  magnet,    (a)  Note  how  much  deflection  is  produced  when  one  of  the  small 
magnets,  say,  an  inch  long,  obtained  by  breaking  the  darning  needle,  is  placed  at  a  given  distance  from 
the  compass ;  then  make  a  stirrup  out  of  copper  wire,  place  the  needle  in  it,  heat  it  to  redness  in  the 
Bunsen  flame,  and  again  test  it  by  means  of  the  compass.    Record  the  effect. 

(6)  Heat  again  to  redness,  and  then  transfer  it  quickly  to  a  position  between  the  poles  of  a  horse- 
shoe magnet.  Let  it  remain  there  until  cool  and  test  again  with  the  compass. 

(<?)  Explain  both  of  the  effects  on  the  assumption  that  magnetization  consists  in  a  particular 
arrangement  of  the  molecular  magnets.  (Remember  that  the  molecules  of  the  needle  are  set  into  vio- 
lent agitation  when  the  needle  is  heated  to  redness.) 

V.  Making  a  magnet  by  induction,    (a)  Hold  a  short  piece  of  unmagnetized  knitting  needle  or 
a  small  steel  nail  parallel  to  the  line  joining  the  poles  of  a  horseshoe  magnet  and  tap  it  vigorously 
with  some  heavy  object  without  allowing  it  to  touch  the  magnet.    Remove  it  and  test  its  poles  with 
the  compass  needle. 

(6)  Turn  it  end  for  end,  replace  it  between  the  poles  of  the  horseshoe  magnet,  and  tap  again. 
Record  the  change  which  you  observe  in  its  poles. 

[65] 


EXPERIMENT  26    (Continued) 

(<?)  Remove  the  steel  rod  from  a  tripod  or  take  one  of  the  small  steel  rods  used  for  bending 
Exp.  13.  Hold  it  nearly  vertical  in  a  north-and-south  plane,  the  upper  end  being  tilted  20°  or  30C 
toward  the  south.  Strike  the  upper  end  three  or  four  sharp  blows  with  a  hammer  and  then  test  the 
two  ends  of  the  rod  for  magnetism.  Note  which  end  is  an  N  pole. 

(d)  Repeat  with  the  ends  of  the  rod  reversed.  Which  end  is  now  an  N  pole  ?  Explain  on  the 
assumption  that  the  molecules  are  permanent  magnets  and  that  magnetization  consists  in  an  alignment 
of  these  molecules. 

From  all  of  the  above  experiments,  what  picture  do  you  make  to  yourself  regarding  the  operations 
which  go  on  within  a  bar  of  iron  when  it  is  magnetized  ?  Draw  a  diagram  to  represent  the  probable 
arrangement  of  the  molecular  magnets  in  a  magnetized  bar,  and  another  to  represent  some  possible 
arrangement  in  an  unmagnetized  bar. 


[66] 


EXPERIMENT  27 
STATIC  ELECTRICAL  EFFECTS 

To  make  an  electroscope,  bend  a  piece  of  No.  18  copper  wire  into  the  form  shown  in  Fig.  45, 
thrust  it  through  a  rubber  stopper,*  hang  a  piece  of  aluminum  foil  about  2  in.  long  over  the  horizontal 
part  of  the  wire,  and  insert  in  a  glass  flask  as  shown.t 

I.  Conductors  and  nonconductors,    (a)  Attach  one  of  the  steel  balls  of  Exp.  3  to  a 
silk  thread  by  means  of  sealing  wax,  or  simply  stick  a  penny  to  the  end  of  a  glass  rod 
with  the  aid  of  sealing  wax.   Such  an  arrangement  is  called  &  proof  plane.    Charge  this 
proof  plane  by  letting  it  rub  along  a  stick  of  sealing  wax  which  has  been  electrified  by 
being  rubbed  with  flannel ;  then  touch  it  to  the  wire  of  the  electroscope.    What  does 
the  instant  divergence  of  the  leaves  show  regarding  the  ease  with  which  a  charge  of 
electricity  passes  through  this  metal  wire  ?    What  does  the  fact  that  the  leaves  stand 

apart  show  regarding  the  nature  of  the  force  which  the  two  parts  of  the  same  charge  going  to  the 
two  leaves  exert  upon  each  other  ? 

(6)  Touch  the  wire  of  the  electroscope  for  an  instant  with  a  piece  of  sealing  wax  which  has  not 
been  electrified.  Touch  it  with  a  wooden  ruler.  Touch  it  with  your  finger.  Which  of  the  three 
conducts  off  the  charge  most  readily  ? 

(<?)  Charge  the  proof  plane,  again  touch  it  with  the  finger,  and  then  try  to  charge  the  electroscope 
with  it.  Explain  why  the  rubbed  sealing  wax  holds  its  charge  when  it  is  held  in  the  hand,  while  the 
proof  plane  loses  its  charge  as  soon  as  it  is  touched  with  the  finger. 

II.  Positive  and  negative  electricity,    (a)  Charge  the  electroscope  as  above,  then  bring  the  charged 
sealing  wax  toward  it.    Record  the  effect  produced  on  the  divergence  of  the  leaves.    Explain  this 
effect  in  view  of  the  fact  that  the  charge  on  the  wire  of  the  electroscope  is  a  part  of  the  charge  which 
was  originally  on  the  sealing  wax  (see  I,  («)). 

(6)  Rub  a  glass  rod  with  silk,  then  bring  it  slowly  toward  the  charged  electroscope.  Record  the 
first  effect  observed.  (If  you  bring  the  rod  too  close,  the  effect  will  be  reversed.)  In  order  to  account 
for  this  effect,  what  sort  of  a  force  must  we  now  assume  the  charge  on  the  glass  rod  to  exert  upon 
the  charge  on  the  electroscope  ? 

A  charge  of  electricity  which  acts  as  does  the  charge  on  a  glass  rod  which  has  been  rubbed  with 
silk  is  arbitrarily  called  a  positive  (-f-)  charge.  A  charge  which  acts  like  the  charge  on  the  sealing  wax 
when  it  has  been  rubbed  with  flannel  is  called  a  negative  (— )  charge. 

(c)  Discharge  the  electroscope,  then  charge  it  with  the  aid  of  the  proof  plane  and  glass  rod, 
precisely  as  you  first  charged  it  with  the  aid  of  the  proof  plane  and  sealing  wax.    Note  and  record 
the  behavior  of  the  leaves  when  you  now  bring  first  the  glass  rod  and  then  the  charged  sealing  wax 
toward  the  electroscope.    In  view  of  all  of  these  observations,  state  how,  in  general,  like  and  unlike 
charges  of  electricity  act  upon  one  another. 

(d)  Charge  the  electroscope  either  positively  or  negatively ;  then  rub  a  piece  of  paper  en  the 
coat  sleeve  and  determine  by  bringing  the  paper  near  the  electroscope  whether  it  has  received  a  +  or 
a  —  charge.    Flick  your  handkerchief  across  the  suspended  steel  ball  and  see  whether  it  has  received 
a  +  or  a  —  charge. 

*  If  the  rubber  stopper  has  not  a  hole  through  it  already,  you  can  easily  make  one  with  a  hot  knitting  needle.  If  it 
already  has  a  hole  which  is  too  large,  cover  the  wire  with  sulphur  or  with  sealing  wax.  This  will  not  only  make  it  fit  but 
will  also  improve  the  insulation. 

t  An  electroscope  so  made  will  hold  its  charge  for  hours,  even  in  summer.  To  cut  the  foil  blow  it  out  flat  on  a  sheet  of 
paper,  lay  another  sheet  on  top  of  it,  leaving  one  edge  uncovered,  and  then  cut  off  a  strip  with  a  sharp  knife  or  razor.  A  saw 
stroke  will  work  best. 

[67] 


EXPERIMENT  27    (Continued) 

III.  To  charge  two  bodies  simultaneously  by  induction.   Hold  two  suspended  steel  balls  in  contact. 
Bring  a  piece  of  electrified  sealing  wax  to  within  an  inch  of  the  balls,  holding  it  in  the  line  joining 
their  centers.    While  it  is  in  this  position  separate  the  two  balls,  then  bring  each  over  a  negatively 
charged  electroscope.    Has  the  ball  which  was  the  nearer  the  sealing  wax  received  a  +  or  a  —  charge  ? 
Which  kind  of  charge  did  the  other  ball  receive  ?    If  an  uncharged  body  contains  equal  amounts  of 
both  positive  and  negative  electricity  which,  under  ordinary  circumstances,  are  so  uniformly  distributed 
that  they  completely  neutralize  each  other,  and  if  one  or  both  of  these  electricities  is  free  to  move 
through  the  body  under  the  influence  of  an  outside  charge,  can  you  account  for  the  eif ects  which  you 
have  observed  ? 

IV.  To  charge  the  electroscope  by  induction.    Bring  the  charged  sealing  wax  near  enough  to  the 
electroscope  to  produce  a  large  divergence.   Remove  the  sealing  wax.   Why,  on  the  above  assumptions, 
do  the  leaves  again  collapse  ?  Again  produce  the  divergence,  but  now  touch  the  finger  to  the  electro- 
scope before  removing  the  wax.    Why  do  the  leaves  collapse  ?    Remove  the  finger,  then  remove  the 
wax.    Why  do  the  leaves  now  diverge  ?    With  the  charged  sealing  wax  find  whether  in  charging 
an  electroscope  by  induction  as  above  the  charge  imparted  to  the  electroscope  is  'like  or  unlike 
that  of  the  charging  body.    Repeat  the  experiment,  using  glass  rod,  and  state  a  general  rule  for  the 
sign  of  the  charge  of  an  electroscope  which  has  been  charged  by  induction.    State  the  rule  for 
charging  by  conduction  (see  I,  (#))• 

V.  To  show  that  a  charge  is  on  the  surface  of  a  conductor  only.    Place  the  inner  vessel  of  a 
calorimeter  on  two  sticks  of  sealing  wax  which  rest  upon  the  table,  then  charge  this  vessel  by  rubbing 
over  it  a  charged  rod  of  any  kind.    Bring  one  of  the  suspended  steel  balls  into  contact  with  the 
outside  of  the  metal  vessel,  then  cause  the  ball  to  approach  the  electroscope.    Has  the  ball  received 
a  charge  ?    Discharge  the  ball  with  the  finger,  then  lower  it  carefully  into  the  metal  vessel  till  it 
rest's  on  the  bottom.    Remove  it  and  see  whether  it  is  now  charged.    Record  your  conclusion.   Why 
was  it  necessary  to  place  the  metal  vessel  on  the  sticks  of 

sealing  wax  ? 

VI.  To   prove   that  +  and  —  electricities  appear  in  equal 
amounts,    (a)  Charge  a  steel  ball  negatively  and  bring  it  care- 
fully inside  of  vessel  A  (Fig.  46),  which  is  connected  by  a 
wire  to  the  electroscope.    The  divergence  of  the  leaves  will 

measure  the  charge  induced  on  the  outside  of  A.    Touch  the 

FIG.  46 
ball  to  the  inner  wall  of  the  vessel.    The  divergence  of  the 

leaves  is  now  a  measure  of  the  charge  which  was  originally  on  the  ball,  for  this  charge  has  all 
passed  to  the  outside  (see  V).  Did  the  divergence  change  at  all  when  the  ball  touched  the  wall  ? 
What  conclusion  do  you  draw  regarding  the  minus  charge  on  the  ball  and  the  minus  charge  induced 
by  it  on  the  outside  of  the  vessel  ? 

(5)  Recharge  the  ball  and  again  hold  it  inside  of  A,  without  touching  the  wall,  and  note  the 
divergence  of  the  leaves.  Touch  the  outside  of  A  with  the  finger.  Remove  the  finger,  then  remove 
the  ball,  but  do  not  discharge  it.  Is  the  deflection  the  same  as  before  ?  Test  the  sign  of  the  charge 
on  the  leaves.  Reinsert  the  ball  and  touch  it  to  the  vessel.  Does  the  electroscope  show  any  charge  ? 
What  conclusion,  then,  do  you  draw  regarding  the  —  charge  on  the  ball  and  the  +  charge  which  was 
induced  on  the  inside  of  A  ? 

VII.  The  principle  of  the  condenser,    (a)  By  means  of  a  wire  connect  the  electroscope  with  a 
vertical  metal  sheet  A  (Fig.  47),  about  4  in.  square,  which  is  nailed  to  a  piece  of  wood  as  shown. 
Support  this  on  two  pieces  of  sealing  wax.    Charge  plate  A  by  giving  it  a  single  stroke  with  a  small 
piece  of  electrified  sealing  wax.    If  the  electroscope  shows  any  leak,  rub  the  sealing-wax  supports  on 
a  cloth  until  they  are  warm.    Now  move  a  second  plate  B,  which  you  keep  in  contact  with  your  hand, 

[68] 


FIG.  47 


EXPERIMENT  27    (Continued) 

up  to  within  about  1  or  2  mm.  of  A.    What  effect  do  you  find  that  this  has  on  the  potential  of  A  ? 
(Consider  potential  to  be  measured  by  the  divergence  of  the  leaves  of  the  electroscope.) 

(6)  Electrify  the  sealing  wax  again,  as  nearly  as  possible  in  the  way  you  did  at  first,  and  give  A 
another  stroke.  Repeat  until  the  original  divergence  is  reestablished.  From  the  number  of  these 
strokes  estimate  roughly  how  many  times  the  electrical  capacity 
of  A  has  been  increased  by  the  presence  of  B;  that  is,  how  many 
tunes  the  original  amount  of  electricity  is  now  required  to  bring 
it  to  the  same  potential  which  it  had  at  first.  In  view  of  the 
fact  that  the  —  charge  on  A  repelled  negative  electricity  to  the 
earth  through  your  finger  and  thus  induced  a  +  charge  on  B, 
can  you  see  why,  when  B  is  near  by,  it  takes  a  larger  charge  on 
A  to  produce  a  given  divergence  than  when  B  is  remote  ? 

(e)  Slip  a  5  x  5  in.  glass  plate  between  A  and  B  and  watch  the  electroscope.  Does  this  increase 
or  decrease  the  potential  of  A  ?  Hence  does  it  increase  or  decrease  the  capacity  of  the  condenser  f 

Push  the  plates  together  until  each  is  in  contact  with  the  glass  plate.  Remove  the  glass  without 
changing  the  distance  between  the  plates,  and  charge  A  to  a  given  divergence.  Insert  the  glass  and 
find  how  many  more  approximately  equal  charges  may  now  be  put  on  A  before  bringing  the  leaves 
to  about  the  same  divergence.  The  ratio  of  the  charge  on  A  when  the  glass  was  in  to  the  charge 
when  the  glass  was  out  is  called  the  specific  inductive  capacity  of  glass. 

VIII.  The  electrophorus.  Charge  the  hard  rubber  plate  B  of  Fig.  48  by  rubbing 
it  with  fur  or  flannel.  Place  metal  plate  A  on  B.  Touch  A  with  your  finger. 
When  touched  what  kind  of  a  charge  will  be  repelled  out  of  A  to  earth  by  the 
negative  on  B  ?  What  kind  will  be  left  on  A  ?  By  means  of  the  insulating  handle 
lift  A  and  bring  it  toward  a  positively  charged  electroscope.  What  happens? 
This  shows  A  to  be  positively  or  negatively  charged?  Try  lighting  a  Bunsen 
burner  by  holding  it  in  the  hand  and  allowing  the  spark  to  pass  off  the  edge  of  A 
to  the  top  of  burner  while  the  gas  is  partly  turned  on.  Does  the  charge  on  A  come  from  B  ?  Give 
reason  for  your  answer.  Why  can  you  charge  A  an  indefinite  number  of  times  in  the  above  manner  ? 
Where  does  the  energy  represented  in  the  spark  which  lights  the  gas  come  from  ? 


FIG.  48 


[69] 


EXPERIMENT  28 


THE  VOLTAIC  CELL 

I.  Action  of  dilute  sulphuric  acid  on  copper  and  zinc  strips,    (a)   Open  circuit.  Fill  a  tumbler  two- 
thirds  full  of  water  and  add  about  one  sixtieth  as  much  sulphuric  acid.   Introduce  into  the  acid  a  strip 
of  zinc  about  a  centimeter  wide  and  observe  and  record  what  effect,  if  any,  is  produced  by  the  acid. 
(The  bubbles  are  hydrogen.) 

Repeat  the  experiment  with  a  similar  strip  of  copper. 

Next  place  both  the  zinc  and  the  copper  in  the  acid  at  the  same  time,  but  take  care  that  they  do 
not  touch  each  other  at  any  point.  Observe  and  record  the  action  at  each  plate. 

(6)  Closed  circuit.  Press  the  tops  of  the  strips  firmly  together  and  notice  what  change,  if  any, 
takes  place  at  the  surface  of  each  metal.  Record  the  results. 

II.  Effect  of  amalgamation.   Dip  the  zinc  plate  into  a  dish  containiag  a  little  mercury  and  rub  the 
mercury  over  the  wet  portion  of  the  zinc  until  it  is  covered  with  a  smooth,  even  coat  of  mercury.   Dip 
the  amalgamated  zinc  into  the  sulphuric  acid  solution  again,  and  repeat  the  observations  of  I,  record- 
ing what  differences,  if  any,  are  observed  in  the  action. 

III.  Effects  observable  about  the  wire  connecting  the  strips,    (a)   For  convenience  in  handling, 
place  strips  of  copper  and  of  amal- 
gamated zinc  in  clamps  such  as 

those  shown  in  Fig.  49  and  connect 
these  clamps  by  means  of,  say, 
No.  24  copper  wire  to  the  binding 
posts  of  the  25-turn  coil  of  No.  22 
wire  on  the  galvanoscope,  after 
placing  the  latter  with  the  plane 
of  its  coils  north  and  south.  Dip 


the  metals  in  the  acid  and  observe 
the  effect  on  the  needle. 

(5)  Disconnect  the  wires  from  the  galvanoscope  and  touch  them  to  the  tongue.  What  evidence  do 
you  obtain  of  some  action  going  on  when  the  plates  are  in  the  acid,  but  which  disappears  as  soon  as 
they  are  lifted  from  it  ? 

IV.  Polarization.  Take  a  fresh  and  dry  copper  plate  or  else  dry  the  old  one  by  heating  it  in  a 
Bunsen  flame  until  it  is  much  too  hot  to  hold  and  then  letting  it  cool.  Insert  the  zinc  and  copper  in 
the  clamps  and  connect  as  before  to  the  25-turn  coil  of  the  galvanoscope,  but  this  time  insert  into  the 
circuit  about  a  meter  of  No.  36  German-silver  wire.  *  (No.  30  will  do,  but  No.  36  is  better.)  Turn  the 
compass  until  the  needle  points  to  0° ;  then  immerse  the  plates  in  the  acid,  and,  as  soon  as  the  needle 
stops  swinging  violently,  read  the  deflection.  (If  this  deflection  is  more  than  40°  or  50°,  slide  the  com- 
pass along  in  the  frame  away  from  the  25-turn  coil,  until  the  deflection  is  reduced  to  50°  or  less.) 
Watch  the  needle  for  a  minute  and  record  what  you  observe.  In  II  you  found  that  if  the  zinc  is 
well  amalgamated,  hydrogen  appears  only  at  the  copper  plate.  Short-circuit  the  cell  for  half  a  minute 
by  holding  a  short  strip  of  copper  in  contact  with  both  the  copper  and  zinc  plates.  This  simply 
enables  the  hydrogen  to  be  generated  in  greater  abundance.  It  brings  the  deflection  nearly  to  0 
because  most  of  the  current  now  goes  through  the  copper  strip.  Remove  the  copper  strip.  Does  the 
deflection  return  quite  to  its  old  value  ?  From  these  experiments  what  effect  do  you  conclude  that 

*  For  the  sake  of  avoiding  loose  German-silver  wire,  it  is  best  to  insert  the  meter  of  No.  36  wire  between  the  binding  post* 
1  and  a  of  Fig.  63,  and  then  to  connect  the  zinc  plate  of  the  cell  to  a,  the  copper  plate  to  one  terminal  of  the  galvanoscope,  and 
the  other  terminal  of  the  galvanoscope  to  1. 

[71] 


EXPERIMENT  28    (Continued) 

the  accumulation  of  hydrogen  upon  the  copper  plate  has  upon  the  strength  of  the  current  which 
the  cell  can  furnish?  This  is  technically  called  the  polarization  of  the  cell,  and  a  cell  in  which  this 
effect  occurs  is  called  a  polarizing  cell. 

V.  A  nonpolarizing  cell.    Replace  the  simple  cell  by  a  Daniell  cell,  or  construct  what  is  essentially 
a  Daniell  cell  as  follows :  First  dry  the  copper  plate  in  the  Bunsen  flame,  then  replace  it  in  its  clamp. 
Fill  the  tumbler  half  full  of  a  saturated  solution  of  copper  sulphate  and  pour  zinc  sulphate  into  a  small 
porous  cup,  which  is  then  to  be  placed  inside  the  tumbler.   Now  immerse  the  plates  in  the  liquids,  the 
zinc  going  into  the  zinc  sulphate  in  the  porous  cup  and  the  copper  into  the  copper  sulphate.    (The  I 
porous  cup  is  simply  to  keep  the  two  liquids  separated.    The  electric  current  can  pass  through  it  with 
ease.)    Watch  the  needle  and  record  its  behavior.    Short-circuit  the  cell  and  see  if  thereafter  the 
deflection  returns  to  its  old  value.    Is,  then,  a  Daniell  cell  a  polarizing  or  a  nonpolarizing  cell  ?    Does 
the  fact  that  the  element  which  is  deposited  on  the  copper  plate  when  it  is  immersed  hi  copper  sul- 
phate is  copper  itself  suggest  to  you  any  reason  why  in  this  case  the  current  is  not  changed,  as  was 
found  to  be  the  case  when  the  deposit  was  hydrogen  ?    In  which  case  is  the  character  of  the  surface 
of  the  plate  changed  by  the  deposit  ? 

VI.  A  polarizing  commercial  ceil.    Replace  the  Daniell  by  a  Leclanche  cell,  if  one  is  available  (a 
dry  cell  will  answer  nearly  as  well).    This  consists  of  a  zinc  rod  in  sal  ammoniac  and  a  carbon  plate 
inside  a  porous  cup  which  is  full  of  manganese  dioxide.    See  first  whether  the  current  which  this  cell 
sends  through  the  three  feet  of  No.  36  German-silver  wire  weakens  at  all  in  two  minutes.     (If  the 
deflection  is  more  than  45°,  push  the  compass  farther  away  or  change  to  the  one-turn  coil.)    Then 
short-circuit  the  cell  for  half  a  minute  and  see  if  thereafter  the  deflection  returns  to  the  old  value.   Is, 
then,  this  cell  polarizing  or  nonpolarizing  ?    Watch  the  needle  for  a  minute  after  the  cell  has  been 
short-circuited.    Does  the  current  gradually  recover  part  of  its  former  strength?    Break  the  circuit 
entirely  and  let  the  cell  stand  for  a  few  minutes ;  then  read  the  deflection. 

Try  the  same  experiment  with  a  simple  cell.  Record  the  difference  in  the  behavior  of  the  two  cells. 
This  difference  is  due  to  the  fact  that  in  the  simple  cell  there  is  nothing  to  remove  the  film  of  hydro- 
gen from  the  surface  of  the  plate  upon  which  it  is  deposited.  In  the  Leclanche  cell,  on  the  other  hand, 
the  manganese  dioxide  slowly  unites  with  the  hydrogen  and  therefore  removes  it  from  the  carbon  plate. 
This  is  indeed  the  object  of  its  use.  A  Leclanche  cell  is,  then,  one  which  recovers  on  open  circuit. 


[72] 


EXPERIMENT  28  A 
THE  VOLTAIC  CELL 


I.  Action  of  dilute  sulphuric  acid  on  copper  and  zinc  strips,    (a)   Open  circuit.    Fill  a  tumbler  two- 
thirds  full  of  water  and  add  about  one  sixtieth  as  much  sulphuric  acid.    Introduce  a  strip  of  zinc 
about  a  centimeter  wide  into  the  acid  and  observe  and  record  what  effect,  if  any,  is  produced  by  the 
acid.    (The  bubbles  are  hydrogen.) 

Repeat  the  experiment  with  a  similar  strip  of  copper. 

Next  place  both  the  zinc  and  copper  in  the  acid  at  the  same  time,  but  take  care  that  they  do  not 
touch  each  other  at  any  point.  Observe  and  record  the  action  at  each  plate. 

(6)  Closed  circuit.  Press  the  tops  of  the  strips  firmly  together  and  notice  what  change,  if  any, 
takes  place  at  the  surface  of  each  metal.  Record  results. 

II.  Effect  of  amalgamation.   Dip  the  zinc  plate  into  a  dish  containing  a  little  mercury  and  rub  the 
mercury  over  the  wet  portion  of  the  zinc  until  it  is  covered  with  a  smooth,  even  coat  of  mercury.   Dip 
the  amalgamated  zinc  into  the  sulphuric  acid  solution  again,  and  repeat  the  observations  of  I,  recording 
what  differences,  if  any,  are  observed  in  the  action. 

III.  Effects  observable  about  the  wire  connecting 
the  strips,    (a)  For  convenience  in  handling,  place 
strips  of  copper  and  of  amalgamated  zinc  in  clamps 
such  as  those  shown  in  Fig.  50. 

Take  about  5  ft.  of  No.  24  copper  wire,  loop  the 
middle  portion  of  it  3  or  4  times  around  a  compass 
in  such  a  way  that  the  plane  of  the  coil  is  north  and 
south,  and  then  connect  the  two  ends  of  the  coil  to 
the  clamps  shown  in  Fig.  50.  Dip  the  metals  in  the 
acid  and  observe  the  effect  on  the  needle. 

(6)  Attach  two  wires  to  the  cell  and  touch  the  ends  of  them  to  the  tongue.  What  evidence  do 
you  obtain  of  some  action  going  on  when  the  plates  are  in  the  acid,  but  which  disappears  as  soon  as 
they  are  lifted  from  it  ? 

IV.  Polarization,    (a)  Take  a  fresh  and  dry  copper  plate,  or  else  dry  the  old  one  by  heating  it  in 
a  Bunsen  flame  until  it  is  much  too  hot  to  hold  and  then  letting  it  cool.    Insert  the  zinc  and  copper 
in  the  clamps  and  connect  them,  as  in  Fig.  50,  to  a  low  reading  ammeter,  by  means  of  two  pieces  of 
No.  30  copper  wire  each  about  1  m.  long.    Now  watch  the  ammeter  reading  closely  and  at  the  same 
time  immerse  the  plates  in  the  acid,  being  sure  to  read  the  highest  amperage  which  the  cell  will 
furnish  when  the  plates  are  first  immersed.    Record  this  reading. 

(6)  Watch  the  ammeter  for  two  minutes  and  record  what  you  observe,  together  with  the  ammeter 
reading  at  the  end  of  the  two  minutes. 

(c*)  Short-circuit  the  cell  for  one  minute  by  holding  a  short  strip  of  copper  in  contact  with  both 
the  copper  and  the  zinc  plate.  This  enables  the  cell  to  furnish  a  larger  current,  but  brings  the 
ammeter  reading  nearly  to  zero  because  most  of  the  current  now  goes  through  the  copper  strip. 
Observe  the  cell  while  it  is  short-circuited  and  note  that  as  this  larger  current  is  drawn  from  the  cell 
it  is  accompanied  by  a  more  rapid  evolution  of  hydrogen  in  the  cell.  Remove  the  copper  strip  and 
then  record  the  ammeter  reading.  Does  the  cell  now  furnish  as  large  a  current  as  it  did  just  before 
it  was  short-circuited  ?  (See  ammeter  reading  in  (£>).) 

From  these  experiments  what  effect  do  you  conclude  that  the  accumulation  of  hydrogen  upon  the 
copper  plate  has  upon  the  strength  of  the  current  which  the  cell  can  furnish  ?  This  is  technically 
called  the  polarization  of  the  cell,  and  a  cell  in  which  this  effect  occurs  is  called  a  polarizing  cell. 


EXPERIMENT  28  A    (Continued) 

V.  A  nonpolarizing  cell,    (a)  Replace  the  simple  cell  by  a  Daniell  cell  or  construct  what  is 
essentially  a  Daniell  cell,  as  follows :   First  dry  the  copper  plate  in  the  Bunsen  flame,  then  replace  it 

-in  its  clamp.  Fill  the  tumbler  half  full  of  a  saturated  solution  of  copper  sulphate  and  pour  zinc 
sulphate  into  a  small  porous  cup,  which  is  then  to  be  placed  inside  the  tumbler.  Now  immerse  the 
plates  in  the  liquids,  the  zinc  going  into  the  zinc  sulphate  in  the  porous  cup  and  the  copper  into  the 
copper  sulphate.  (The  porous  cup  is  simply  to  keep  the  two  liquids  separated.  The  electric  current 
can  pass  through  it  with  ease.)  As  in  IV,  watch  the  ammeter  reading  for  two  minutes.  Short-circuit 
the  cell  for  one  minute  and  see  if  thereafter  the  ammeter  reading  returns  to  its  old  value. 

Is,  then,  a  Daniell  cell  a  polarizing  or  a  nonpolarizing  cell?  Does  the  fact  that  the  element  which 
is  deposited  on  the  copper  plate  when  it  is  immersed  in  copper  sulphate  is  copper  itself  suggest  to  you 
any  reason  why  in  this  case  the  current  is  not  changed,  as  was  found  to  be  the  case  when  the  deposit 
was  hydrogen  ?  In  which  case  is  the  character  of  the  surface  of  the  plate  changed  by  the  deposit  ? 

VI.  A  polarizing  commercial  cell.    Replace  the  Daniell  cell  by  either  a  Leclanche  or  a  dry  cell. 
Record  (a)  the  current  when  the  cell  is  first  connected  to  the  ammeter ;  (5)  the  current  at  the  end  of 
two  minutes ;  (<?)  the  current  after  the  cell  has  been  short-circuited  for  half  a  minute. 

Is  this  cell  polarizing  or  nonpolarizing  ? 

Watch  the  ammeter  for  the  minute  following  the  removal  of  the  short  circuit.  Does  the  cur- 
rent gradually  recover  part  of  its  former  strength  ?  Break  the  circuit  entirely  and  let  the  cell  stand 
for  three  or  four  minutes ;  then  record  the  ammeter  reading. 

Try  the  simple  cell  used  in  IV  and  see  if  it  will  recover  any  of  its  strength  after  being  short- 
circuited.  What  is  the  difference  in  the  behavior  of  these  two  polarizing  cells  ?  This  difference  is 
due  to  the  fact  that  in  the  simple  cell  there  is  nothing  to  remove  the  film  of  hydrogen  from  the  sur- 
face of  the  plate  upon  which  it  is  deposited.  In  either  the  Leclanche  or  the  dry  cell,  on  the  other 
hand,  the  manganese  dioxide  slowly  unites  with  and  therefore  removes  the  hydrogen  from  the  carbon 
plate.  This  is  indeed  the  object  of  its  use.  A  Leclanche  or  a  dry  cell  is,  then,  one  which  recovers  on 
open  circuit. 


[74] 


EXPERIMENT  29 


FIG.  61 


MAGNETIC  EFFECT  OF  A  CUKRENT    . 

I.  The  right-hand  rule,  or  Ampere's  rule.  Since  a  wire  through  which  a  current  is  flowing  has  just 
been  found  to  deflect  a  magnetic  needle  held  near  it,  the  wire  must  be  surrounded  by  magnetic  lines 
of  force.  The  direction  in  which  the  N  pole  of  the  magnetic  needle  tends  to  move  gives,  by  definition,  the 
direction  of  these  magnetic  lines. 

The  direction  in  which  the  positive  electricity  flows  through  the  circuit  of  a  zinc-copper  cell  is  from 
zinc  to  copper  inside  the  liquid  and  from  copper  to  zinc  in  the  connecting  wire ;  that  is,  it  flows  in  the 
direction  in  which  the  hydrogen  was  found  to  move  in  the  last  experiment.    We  know  this  because  a 
very  delicate  electroscope  will  show  that  on  open  circuit  the  copper  plate 
acquires  a  small  +  charge  of  static  electricity  and  the  zinc  a  small  — 
charge.    For  this  reason  the  copper  or  carbon  plate  of  a  voltaic  cell  is 
always  called  the  plus  (+)  plate  and  the  zinc  the  minus  (— )  plate.    The 
direction  of  an  electric  current  is  defined  as  the  direction  in  which  the 
positive  electricity  moves. 

By  the  series  of  experiments  given  below,  test  the  following  rule  :  If  the  conductor  is  grasped  ly  the 
right  hand  so  that  the  thumb  points  in  the  direction  in  which  the  current  flows,  then  the  magnetic  lines  of  force 
oass  in  concentric  circles  around  the  wire  in  the  direction  in  which  the  fingers  of  the  hand  encircle  it  (Fig.  51). 

(#)  Connect  either  a  simple  cell  or  a  dry  cell  in  the  manner  shown  in  Fig  52,  so  that  the  current 
will  flow  from  the  copper  (or  carbon)  through  the  commutator  C,  then  over  the  needle  from  south  to 
north,  and  back  through  the  commutator  to  the  zinc.  All  of  the  connecting  wires  should  be  copper 
(for  example,  No.  24),  and  that  to  the  right  of  the  commutator  should  be  10  or  12  ft.  long.  Insert 
the  top  of  the  commutator  and  record  the  direction  in  which  the  north  pole  of  the  needle  turns, 

(5)  Turn  the  top  of  the  commutator  through  90°,  so  that  the  mercury  cup  a  is  connected  to  e 
and  b  to  d,  instead  of  a  to  b  and  e  to  d.   This  reverses  the  current  in  the  wire  so  that  it  goes  over  the 
needle  from  north  to  south.    Record 
the  effect  on  the  needle  and  com- 
pare with  Ampere's  rule. 

(<?)  Place  the  compass  above  the 
wire  without  changing  the  direction 
of  the  current,  and  compare  with 
the  rule  the  effect  produced  on  the 
needle.  Reverse  the  direction  of  the 
current  by  means  of  the  commu- 
tator and  again  compare. 

(cT)  Hold  the  wire  so  that  the 
current  flows  vertically  dowmvard 
just  in  front  of  the  N  pole  of  the 
compass ;  then  cause  the  current  to  flow  upward  past  the  same  pole,  and  test  the  rule  in  each 

(<?)  Hold  the  wire  so  that  the  current  flows  from  west  to  east  over  the  middle  of  the  needle. 

Does  the  experiment  show  that  the  lines  of  magnetic  force  lie  in  planes  at  right  angles  to  the 
direction  of  the  wire  ?  How  ? 

II.  To  find  the  direction  of  an  unknown  current.  Let  the  instructor  bring  a  current  the  direction  of 
which  is  unknown  into  the  laboratory  by  a  wire  connected  with  a  cell  in  a  closet  or  in  an  adjoining  room. 
Hold  a  compass  needle  near  the  wire  and  determine  the  direction  in  which  the  current  is  flowing  in 
the  wire.  Record  your  result  and  then  test  the  correctness  of  it  by  following  the  wire  to  the  cell 

[75] 


FIG.  52 


EXPERIMENT  29    (Continued) 

III.  The  effect  of  loops,  (a)  As  in  I,  pass  a  current  from  a  cell  over  the  compass  from  south  to 
north,  keeping  the  wire  as  close  to  the  face  of  the  compass  as  possible.  Note  the  amount  of  deflection, 
If  this  is  more  than  4°,  introduce  enough  German-silver  wire  to  make  the  deflection  just  4°.  Then 
cause  the  wire  to  return  beneath  the  needle,  so  that  a  loop 
is  formed,  in  the  upper  part  of  which  the  current  flows 
past  the  needle  from  south  to  north,  and  in  the  lower  part 
from  north  to  south.  Again  note  the  amount  of  deflection. 
How  do  you  account  for  this  last  deflection  ? 

(b~)  Loop  the  wire  two  and  then  three  times  around  the  compass  in  such  a  way  that  the  plane  of 
the  coil  is  north  and  south  and  record  the  deflection  in  each  case.  What  change  is  produced  in  the 
deflection  by  each  new  turn  ?  Explain. 

(c)  Try  the  effect  of  placing  both  sides  of  the  loop  above  the  needle,  as  in  Fig.  53.  Explain  the 
observed  effect. 


FIG.  53 


RECORD   OF  EXPERIMENT 


DIRECTION  OF 
CURRENT 

POSITION  OF 

COMPASS 

JV  POLE  OF  NEEDLE  is 
DEFLECTED  TOWARD 

I,  (a) 

South  to  north 

Under  wire 

(*) 

North  to  south 

Under  wire 

(') 

North  to  south 

Above  wire 

w 

Vertically  down 

South  of  wire 

Vertically  up 

South  of  wire 

II 

III,  (a) 

South  to  north 

Under  wire 

Deflection  =                        .     ° 

Around  1  loop 

Between  wires 

Deflection  =  ° 

(b) 

Around  2  loops 

Between  wires 

Deflection  =            ° 

Around  3  loops 

Between  wires 

Deflection  =                        .  .  ° 

(c} 

As  in  Fig.  53 

See  Fig.  53 

Deflection  =  ° 

[76] 


EXPERIMENT  30 


FIG.  64 


I.  Magnetic  effect  of  a  helix,    (a)  Having  the  circuit  arranged  as  in  Fig.  52,  the  current  being 
furnished  either  by  a  simple  cell  or  by  a  dry  cell,  form  a  close  helix  (see  Fig.  54)  by  wrapping  the 
conducting  wire  forty  or  fifty  times  around  a  lead  pencil.    Then  with  the  aid 

of  the  compass  see  whether  or  not  the  helix  is  a  magnet ;  that  is,  whether  one 
end  of  it  attracts  the  north  pole  while  the  other  repels  it. 

(£)  By  means  of  the  commutator  reverse  the  direction  of  the  current  through 
the  helix  and  record  what  effect  is  thus  produced  upon  the  poles. 

(c)  Test  the  following  rule  for  determining  the  poles  of  a  helix  :    If  the  helix 
is  grasped  in  the  right  hand  so  that  the  fingers  are  pointing  in  the  direction  in  which 
the  current  is  flowing  in  the  coils  (see  Fig.  55),  the  thumb  will  point  in  the  direction  of  the  magnetic  lines 
of  force  ;  that  is,  the  thumb  ivill  point  towards  the  north  pole  of  the  helix.    Show  how  this  rule  follows 
from  Ampere's  rule. 

II.  The  principle  of  the  electromagnet,    (a)  Thrust  an  unmagnetized  soft-iron  rod  (for  example, 
a  wire  nail)  into  the  helix  and  then  test  the  nail  and  helix  together  in  the  same  way  in  which  the 
helix   alone  was  tested  in  the   preceding   experiment.    Are   the   poles 

stronger  or  weaker  than  before  ? 

(6)  Reverse  the  current  by  means  of  the  commutator  and  test  and 
record  the  effect  on  the  poles. 

(c)  Bend  a  piece  of  large  iron  wire  into  the  shape  of  a  letter  U  and 
mark  one  end  with  chalk.  About  the  ends  of  both  arms  of  the  U  wind  a 
wire  carrying  a  current,  in  such  a  way  that  the  marked  end  of  the  U  shall  be 
an  N  magnetic  pole  and  the  other  an  S  pole.  Test  by  means  of  a  compass. 

III.  Use  of  the  electromagnet  in  an  electric  bell,     (a)    Connect  an 
electric  bell  with  a  dry  cell,  and  with  an  inexpensive  compass  test  the 

condition  of  the  electromagnet,  first  when  the  clapper  is  held  against  the  bell,  then  when  it  is  held 
away  from  it.  Trace  the  current  through  the  instrument  and,  with  the  aid  of  a  diagram,  explain  in. 
your  notebook  why  the  bell  rings. 

(6)  Connect  a  bell,  two  push 
buttons,  and  a  cell  in  such  a  way 
that  pushing  either  button  will  ring 
the  bell. 

IV.  Principle  of  the  D'Arsonval 
galvanometer,    (a)  Hang  a  coil  of 
about  one  hundred  and  seventy-five 
turns  of  No.  32  copper  wire  between 
the  poles  of  a  horseshoe  magnet  in 
the  manner  shown  in  Fig.  56,  so  that 

the  plane  of  the  coil  is  parallel  to 

r  FIG.  56 

the  line  joining  the  poles.    The  two 

wires  which  run  from  the  coil  up  to  the  cork  support  should  be  of  No.  40  insulated  copper,  and  one  of 
them  should  be  twisted  about  the  other  loosely,  as  in  the  figure.  Pass  a  current  from  a  cell,  first 
through  a  commutator  and  then  through  the  coil.  Record  the  effect  observed  in  the  coiL 


FIG.  55 


EXPERIMENT  30    (Continued) 

(6)  Reverse  the  direction  of  the  current  and  observe  the  effect  produced.  Explain  why  the  coil 
turns  as  it  does,  remembering  that  it  is  nothing  but  a  flat  helix. 

(<?)  By  rotating  the  cork  at  the  top,  set  the  coil  between  the  poles  of  the  magnet  in  such  a  way 
that  its  plane  is  perpendicular  to  the  line  joining  these  poles.  Turn  on  the  current  and  note  the  effect,  j 

(d)  Reverse  the  current  and  note  again  the  effect.    Explain  in  each  case  the  effect  observed. 

Questions,  a.  As  you  look  at  the  N  pole  of  an  electromagnet  does  the  current  encircle  it  in  a  clockwise 
or  counterclockwise  direction  ? 

b.  Devise  an  experiment  by  means  of  which  you  could  make  a  permanent  magnet  without  the  use  of  a 
magnet. 

c.  Name  two  or  three  instruments  or  machines  which  make  use  of  the  electromagnet. 

d.  In  IV,  (d),  when  the  current  through  the  coil  was  reversed,  the  coil  made  a  half  turn.  If  the  coil  were 
free  to  turn,  as  in  a  motor,  would  it  be  possible  to  get  continuous  rotation  of  the  coil  by  reversing  the  cur- 
rent through  the  coil  at  the  proper  times  ? 


EXPERIMENT  31 
UPON  WHAT  DOES  THE  ELECTROMOTIVE  FOECE  (E.M.F.)  OF  A  CELL  DEPEND? 

In  the  present  experiment  we  shall  compare  the  electromotive  forces,  or  the  electric  pressures,  which 
cells  of  different  form  are  able  to  maintain,  by  comparing  the  currents  which  they  can  force  through 
coils  of  comparatively  high  resistance :  that  is,  through  voltmeters. 

I.  Effect   of   size   of   plates   and   distance   between   them   on   the   electromotive  force  of  a  cell. 
(a)  Connect  the  zinc  and  the  copper  strip  of  a  simple  cell  to  a  low-reading  voltmeter  as  shown  in 
Fig.  57.    Lower  the  plates  about  2  or  3  cm.  into  the  sulphuric-acid  solution  and  note  the  reading  of 
the  voltmeter. 

(ft)  Lower  the  plates  into  the  solution  until  the 
plate  holder  rests  on  the  glass  and  again  note  the 
reading  of  the  voltmeter. 

(<?)  Remove  the  copper  plate  from  its  holder  and 
press  the  wire,  which  was  attached  to  the  holder, 
against  the  copper  strip.  Now  observe  the  voltmeter 
reading  when  the  copper  strip  is  held  as  far  away 
from  the  zinc  as  is  possible  in  the  tumbler,  and  again 

when  it  is  held  very  close  to,  but  not  touching,  the  F      5- 

zinc  strip. 

What  conclusions  do  you  draw  in  regard  1,0  the  effect  of  the  distance  between  the  plates  and  the 
area  of  immersion  of  the  plates  on  the  electromotive  force  of  a  cell  ? 

II.  Effect  of  different  metal  plates  on  the  electromotive  force  of  a  cell,    (a)  Substitute  a  lead  plate 
for  the  copper  one  and  record  the  E.M.F.  of  this  cell  as  read.on  the  voltmeter.    Record  also  which  metal 
is  4-  and  which  is  — .    (Remember  that  the  metal  connected  to  the  +  marked  binding  post  of  the  volt- 
meter is  +,  and  that  the  one  connected  to  the  —  marked  binding  post  is  the  —  one.)    Record  the  E.M.F. 
of  the  cell  when  the  following  plates  are  used:  zinc-copper,  zinc-lead,  zinc-carbon,  and  zinc-aluminum. 

(b)  Replace  the  zinc  by  a  lead  plate  and  record  the  E.M.F.  produced  by  lead-copper,  lead- 
aluminum,  and  lead-carbon. 

Do  you  see  any  connection  between  the  results  in  (a)  and  (5)  which  enables  you  to  predict  all 
the  results  in  (b~)  from  those  in  (a)? 

(e)  If  so,  arrange  these  five  substances  in  a  list  such  that  each  substance  will  be  positive  with 
respect  to  any  substance  following  it  in  the  list,  but  negative  with  respect  to  any  substance  preceding 
it.  Which  pair  gives  the  highest  E.M.F.  ? 

What  conclusion  do  you  draw  in  regard  to  the  effect  on  the  E.M.F  of  the  kind  of  plates  used  ? 

III.  Effect  of  different  liquids  (electrolytes)  on  the  E.M.F.  of  a  cell,    (a)  Record  the  E.M.F.  pro 
duced  when  zinc  and  copper  are  immersed  (1)  in  dilute  sulphuric  acid  (H2SO4);  (2)  in  a  solution 
of  common  salt,  that  is,  sodium  chloride  (NaCl);   (3)  in  a  solution  of  sodium  carbonate  (Na.pOg); 
(4)  in  common  water  (H2O). 

Rinse  the  plates  thoroughly  before  placing  them  in  a  new  liquid. 

(ft)  Now  record  the  E.M.F.  and  the  sign  of  the  plates  when  copper  and  iron  are  immersed  (1)  in 
dilute  sulphuric  acid;  (2)  in  a  weak  solution  of  ammonium  sulphide  ((NH4)2S)  —  about  20  drops 
in  a  tumbler  of  water  will  do.  What  effect  has  the  change  in  the  liquid  had  upon  the  direction  of 
the  E.M.F.? 

What  conclusion  do  you  draw  in  regard  to  the  effect  of  the  electrolyte  on  the  direction  and 
magnitude  of  the  E.M.F.  of  a  cell? 

[79] 


0 


z 


HH 


FIG.  58 


FIG.  59 


EXPERIMENT  31   (Continued) 

IV.  Effect  of  series  and  of  parallel  connection  on  the  E.M.F.  of  the  combination.   (<z)  Join  two  simple 
cells  or  dry  cells  in  series  (that  is,  the  zinc,  Z,  of  one  to  the  copper  or  carbon,  C,  of  the  other  (Fig.  58)), 
and  record  the  E.M.F.  of  the  combination  when  connected  to  the  voltmeter. 

Record  also  the  E.M.F.  of  each  cell  alone.    Compare  the  E.M.F.  of  the 
two  cells  when  connected  in  series  with  that  produced  by  a  single  cell. 

(5)  Connect  the  two  similar 
cells  in  parallel  (that  is,  zinc  to  zinc 
and  copper  to  copper),  connect  to 
the  voltmeter  as  in  Fig.  59,  and 

record  the  E.M.F.  of  the  combina-      ^  '  v 

tion.  How  does  the  E.M.F.  of  the 
two  cells  in  parallel  compare  with 
that  of  a  single  cell  ? 

What  conclusions  do  you  draw  as  to  the  effects  of  series  and  of  parallel  connections  on  E.M.F.? 

V.  Electromotive  forces  of  various  commercial  cells.    With  the  voltmeter  measure  'the  E.M.F.  of 
several  commercial  cells  such  as  the  Daniell  cell,  dry  cell,  Leclanche  cell,  etc. 

RECORD  OF  EXPERIMENT 

I.  (a)  Metals  immersed  2  or  3  cm.,  E.M.F.  = volts. 

(ft)  Metals  completely  lowered,  E.M.F.    = volts. 

(c)  Metals  far  apart,  E.M.F.  = volts. 

Metals  close  together,  E.M.F.  = volts. 

II.  (a)  Zinc  — ,  copper +,  E.M.F.  =  volts. 

Zinc ,  lead  ,  E.M.F.  = volts. 

Zinc  ,  carbon ,  E.M.F.  = volts. 

Zinc  ,  aluminum ,  E.M.F.  = volts. 

(ft)  Lead ,  copper        ,  E.M.F.  = volts. 

Lead ,  aluminum ,  E.M.F.  =  volts. 

Lead ,  carbon        ,  E.M.F.  = volts. 

(c)  Order  of  metals  such  that  each  is  +  with  respect  to  any  following  it : 
carbon, ,   ,  ,  zinc. 

III.  (a)  Zinc-copper,  in  H2SO4,  E.M.F.    = volts;  in  NaCl,  E.M.F.  =  volts; 

in  Na2CO8,  E.M.F.  = volts ;  in  H2O,  E.M.F.   = volts. 

(6)  Copper ,  iron ,  in  H2SO4,  E.M.F.      = volts. 

Copper ,  iron ,  in  (NH4)2S,  E.M.F.  = volts. 

IV.  (a)  E.M.F.  of  2  cells  in  series      = volts;  of  cell  1  =  volts;  of  cell  2  =  volts 

(ft)  E  M.F.  of  2  cells  in  parallel  = volts. 

Y.          E.M.F.  of  Daniell  cell  = volts ;  of  cell  = volts ; 

of cell  =  '.'. volts ;  of  cell  = volts. 


[80] 


EXPERIMENT  31  A 


UPON  WHAT  DOES  THE  ELECTROMOTIVE  FORCE  (E.M.F.)  OF  A  CELL  DEPEND? 

In  the  present  experiment  we  shall  compare  the  electromotive  forces,  or  the  electric  pressures,  which' 
cells  of  different  form  are  able  to  maintain,  by  comparing  the  currents  which  they  can  force  through 
a  long  piece  of  fine  wire  (a  large  resistance). 

I.  Effect  of  size  of  plates  and  distance  between  them  on  the  electromotive  force  of  a  cell.   To  one  of 
the  terminals  of  the  100-turn  coil  of  the  galvanoscope  connect  a  small  coil  R  (Fig.  60)  of  German- 
silver  wire  the  resistance  of  which  is  about  1000  ohms.    Then  complete  the  circuit  of  the  simple  cell 
through  this  high-resistance  gal- 
vanometer in  the  manner  shown, 

and  read  the  deflection  of  the 
needle.  If  it  is  more  than  20°, 
push  the  compass  farther  away 
from  the  coil.  Lift  the  plates 
almost  out  of  the  liquid  and  read 
again.  Disconnect  the  wires  from 
the  binding  posts  of  the  cell,  re- 
move the  frame  and  plates  from 
the  tumbler,  press  the  wires  very 

firmly  against  much  narrower  zinc  and  copper  strips  than  those  used  before,  immerse  these  in  the 
liquid,  and  read  again.  Place  these  strips  as  far  apart  in  the  tumbler  as  you  can,  and  see  if  the 
deflection  changes  as  you  move  them  together.  (In  all  cases  in  which  accurate  readings  of  deflections 
are  to  be  taken  it  is  desirable  to  tap  the  frame  of  the  galvanometer  lightly  with  a  pencil  so  as  to  over- 
come any  tendency  which  the  needle  may  have  to  stick.) 

What  conclusion  do  you  draw  in  regard  to  the  effect  of  the  distance  between  the  plates  and  of 
the  area  of  immersion  of  the  plates  on  the  electromotive  force  of  a  cell? 

II.  Effect  of  different  metal  plates  on  the  electromotive  force  of  a  cell,    (a)  Without  changing 
anything  else  in  the  circuit,  insert  in  the  clamp  of  the  simple  cell  a  lead  plate  in  place  of  the 
copper  plate  of  the  above  experiment.    If  the  needle  is  deflected  in  the  same  direction  as  before,  we 
may  know  that  in  the  external  circuit  the  current  flows  from  the  lead  to  the  zinc,  that  is,  that  lead 
in  sulphuric  acid  is  +  with  respect  to  zinc ;  but  if  the  needle  turns  in  the  opposite  direction,  then 
the  zinc  is  +  with  respect  to  the  lead.    Record  tests  with  zinc-lead,  zinc-carbon,  and  zinc-aluminum 
electrodes. 

(&)  Replace  the  zinc  plate  by  one  of  lead,  and  record  tests  on  lead-copper,  lead-aluminum,  and 
lead-carbon  electrodes. 

(c)  Do  you  see  any  connection  between  the  results  in  (a)  and  (6)  which  enables  you  to  predict 
all  the  results  in  (6)  from  those  in  (a)  ?  If  so,  arrange  these  five  substances  in  a  list  such  that  each 
substance  will  be  positive  with  respect  to  any  substance  following  it  in  the  list,  but  negative  with 
respect  to  any  substance  preceding  it.  Which  pair  give  the  highest  E.M.F.  ?  What  conclusion  do 
you  draw  in  regard  to  the  effect  on  the  E.M.F.  of  the  kind  of  plates  used  ? 

III.  Effect  of  different  liquids   (electrolytes)  on  the  E.M.F.    (a)  Measure  the  deflection,  using 
the  same  galvanoscope,  when  zinc  and  copper  are  immersed  (1)  in  dilute  sulphuric  acid  (H2SO4) ; 
(2)  in  a  solution  of  common  salt  (NaCl,  that  is,  sodium  chloride);  (3)  in  a  solution  of  sodium 
carbonate  (Na2CO8);  (4)  in  tap  water  (H2O).    Rinse  the  plates  thoroughly  before  placing  them  in 
a  new  liquid. 

[81] 


EXPERIMENT  31  A  (Continued) 


FIG.  61 


(b*)  Now  place  copper  and  iron  strips  in  the  clamps  of  the  cell,  immerse  in  the  sulphuric  acid 
solution,  and  read  ;  then  immerse  the  same  strips  in  a  weak  solution  of  ammonium  sulphide  ((NH4)2S) 
—  about  20  drops  in  a  tumbler  of 
water  will  do.  What  effect  has  the 
change  in  the  liquid  had  upon  the 
direction  of  the  current  ? 

What  conclusion  do  you  draw 
in  regard  to  the  effect  of  the  electro- 
lyte on  the  direction  and  magnitude 
of  the  E.M.F.  of  a  cell  ? 

IV.  Effect  of  series  and  of  parallel 
connection  on  the  E.M.F.  of  the  com- 
bination,   (a)  Connect  the  high-resistance  circuit  to  the  terminals  of  a  single  cell  and  read  the  deflec- 
tion.  If  this  is  more  than  8°  or  10°,  push  the  compass  away  from  the  coil  until  it  is  reduced  to  about 
this  value.    (The  object  of  making  the  deflection  small  is  to  arrange  the  conditions  so  that  the  E.M.F. 
may  be  taken  as  proportional  to  the  deflections.) 

(6)  Join  two  similar  cells  in  series,  that  is,  the 
zinc  of  one  to  the  copper  of  the  other  (Fig.  61),  and 
read  the  deflection  when  connected  to  the  same  circuit. 

(c)  Connect  the  two  similar  cells  in  parallel,  that 
is,  zinc  to  zinc  and  copper  to  copper  (Fig.  62),  again 
read  the  deflection,  and  compare  with  that  produced 
by  a  single  cell. 

What  conclusions  do  you  draw  in  regard  to  the 
effects  of  series  and  of  parallel  connections  on  E.M.F.  ? 

V.  Electromotive  forces  of  various  commercial  cells.    Having  the  galvanometer  circuit  arranged  as 
in  Fig.  56,  reduce  the  deflection  produced  by  a  Daniell  cell,  improvised  as  in  Exp.  28,  V,  to  about 
10°  by  moving  the  compass  away  from  the  coil ;  then  find  the  deflections  produced  by  a  dry  cell,  a 
Leclanche  cell,  and  any  other  cells  which  you  may  have,  and  calculate  the  E.M.F.  of  all  the  latter 
cells  on  the  assumption  that  the  E.M.F.  of  a  Daniell  cell  is  1.08  volts.   In  this  work,  however,  be  very 
careful  not  to  change  the  galvanoscope  in  any  way  during  any  of  the  operations. 

RECORD  OF  EXPERIMENT 

I.          Deflection,  plates  immersed  = °,  plates  partly  immersed  = °, 

For  narrow  strips  far  apart  =  °,  close  together  = °. 


FIG.  62 


METALS  USED 

ELECTROLYTE 

DEFLECTION 

METALS  USED 

ELECTROLYTE 

DEFLECTION 

II.  (a) 

Zinc  —     copper  + 

H2S04 

III.  (a) 

Zinc  .  .  .       copper  .  .  . 

II2S04 

Zinc  .  .  .    lead  .  .  . 

H2SO4 

Zinc  .  .  .       copper  .  .  . 

NaCl 

Zinc  .  .  .    carbon  .  .  . 

H2S04 

Zinc  .  .  .       copper  .  .  . 

Na.2COs 

Zinc  .  .  .    aluminum  .  .  . 

H2S04 

Zinc  .  .  .       copper  .  .  . 

H2O 

(Z>) 

Lead  .  .  .  copper  .  .  . 

H2S04 

(*) 

Copper  .  .  .  iron  .  .  . 

H2S04 

Lead  .  .  .  aluminum  .  .  . 

H2S04 

Copper  .  .  .  iron  .  .  . 

(NH,)2S 

Lead  .  .  .  carbon  .  .  . 

H2SO4 

IV.  (a)  Deflection  for  a  single  cell  =  °,  (ft)  for  2  cells  in  series  = °,  (c)  for  2  cells 

V.         Deflection  for  a  Daniell  cell  = ,    for  a  Leclanch6  cell  = °,  for  a  .... 

E.M.F.  of  a  Daniell  cell  =1.08  volts,  .-.  of  a  Leclanch6  cell   =      volts,  .-.  of  a 

[82] 


in  parallel 

cell  =  .. 

cell    =  . 


.  volts. 


EXPERIMENT  32 


HOW  DOES  THE  RESISTANCE  OF  ELECTRICAL  CONDUCTORS  DEPEND  UPON  THE 
LENGTH,  DIAMETER,  MATERIAL,  AND  METHOD  OF  CONNECTION? 

I.  Length,  (a)  Connect  two  dry  cells  or  a  storage  battery  in  series  with  a  key,  K,  an  ammeter,  and 
100  cm.  of  No.  30  German-silver  wire  (wire  1  of  Fig.  63).  Close  the  key  and  record  the  ammeter 
reading  and  the  voltmeter  reading 
when  the  voltmeter  is  connected 
across  50  cm.  of  the  wire. 

By  Ohm's  law,  the  resistance  I  Ammeter] 

of  any  portion  of  a  circuit  is  given 
by  the  equation 

potential  difference 
Resistance  = , 


or 


Ohms  = 


current 
volts 


,' 

_^--"                                           ~-\ 

61 

/                                                  aX 

o2 

fen 

o3 

cn 

o4 

FIG.  63 


amperes 

Compute  and  record  the  resist- 
ance of  the  50  cm.  of  wire. 

(5)  Take  observations  with  the 

voltmeter  connected  across  the  100  cm.  of  wire  and  compute  its  resistance.    Call  this  resistance  R^ 

(c)  State  the  law  proved  by  I,  (a)  and  I,  (5). 

II.  Diameter,    (a)  Determine  the  resistance  of  100  cm.  of  No.  24  German-silver  wire  (wire  2  of 
Fig.  63).    Call  this  resistance  Rz. 

1(5)  See  Appendix  B  for  diameter  of  wires  used  or  measure  them  with  a  micrometer  caliper. 
(c)  Compute  the  ratios  indicated  hi  the  data  record. 
(d)  State  the  law  proved  by  these  ratios. 
III.  Material,    (a)  Determine  the  resistance  of  100  cm.  of  No.  30  iron  wire  (wire  3  of  Fig.  63). 
Call  this  resistance  R0. 

(b~)  Find  the  resistance  of  100  cm.  of  No.  30  copper  wire  (wire  4  of  Fig.  63).   Call  this  resistance  R^ 
(<?)  The  resistance  of  iron  wire  is  how  many  times  that  of  copper  wire  of  the  same  diameter  and 
gth  ?    (Compare  III,  (a)  and  III,  (6).) 

The  resistance  of  German-silver  wire  is  how  many  tunes  that  of  copper  wire  of  the  same  size  ? 
(Compare  I,  (6)  and  III,  (&).) 

IV.  Series  connection,    (a)  Join  the  left-hand  ends  of  wires  2  and  3  with  a  piece  of  No.  16  or 
No.  18  copper  wire.    (The  resistance  of  this  piece  is  so  small  (see  Appendix  B)  that  it  may  be 
neglected.) 

Connect  the  two  ends  b  and  c  into  the  circuit  and  determine  the  joint  resistance  of  the  two  wires 
in  series. 

(6)  What  is  the  sum  of  the  resistances  of  wires  2  and  3  as  determined  in  II,  (a)  and  III,  (a)? 
(c)  Compare  this  sum  with  the  joint  resistance  in  series  determined  in  IV,  (a). 

(cf)  State  the  law  for  series  connection. 

V.  Parallel,  or  shunt,  connection,    (a)  Join  the  left-hand  ends  and  also  the  right-hand  ends  of 
wires  2  and  3  with  pieces  of  No.  16  or  No.  18  copper  wire.    Send  the  current  in  at  b  or  c  and  out  at 
2  or  3.    Connect  the  voltmeter  across  the  two  wires  thus  connected  in  parallel  in  the  circuit.    Deter- 
mine their  joint  resistance  in  parallel. 

(J)  Determine  the  joint  resistance  of  wires  1,  2,  and  3  in  parallel. 

[83] 


EXPERIMENT  32   (Continued} 

(<?)  Check  the  result  found  in  (a)  by  use  of  the  equation  —  = 1 .    (See  textbook.) 

R      R       R 

(c?)  Check  the  result  found  in  (6)  by  the  equation  —  = 1 1 

Questions,  a.  With  a  given  "head"  of  water  in  a  standpipe,  how  will  the  quantity  of  water  per  second 
which  can  flow  out  of  one  main  compare  with  that  which  can  flow  out  of  another  main  of  twice  the  diameter 
when  the  speeds  with  which  the  water  flows  along  the  mains  are  the  same  in  both  cases  ? 

b.  With  a  given  difference  in  electrical  pressure  (P.D.),  how  will  the  quantity  of  electricity  per  second, 
or  current,  which  will  flow  through  one  wire  compare  with  that  which  will  flow  through  another  wire  of  the 
same  length  and  material  but  of  twice  the  diameter  ? 

c.  Given  three  10-ohm  coils.    Show  by  diagram  how  you  would  connect  them  into  an  electrical  circuit 
so  as  to  introduce  15  ohms  into  the  circuit. 

d.  What  is  the  joint  resistance  of  three  coils  of  5,  10,  and  15  ohms,  respectively,  when  connected  in 
series  ?  when  connected  in  parallel  ? 

RECORD  OF  EXPERIMENT 


WlKE 

LENGTH  AND 
NUMBER 

P.D.  IN  VOLTS 

CURRENT  IN 
AMPERES 

RESISTANCE  IN 

OHMS 

I.  (a)  One-half  wire  1,  German  silver 

50  cm.  No.  30 

(ft)  Wire  1,  German  silver 

100  cm.  No.  30 

*1 

II.  (a)  Wire  2,  German  silver 

100  cm.  No.  21 

R2 

III.  (a)  Wire  3,  iron 

100  cm.  No.  30 

R3 

(b)  Wire  4,  copper 

100  cm.  No.  30 

*4 

IV.  (a)  Wires  2  and  3  (series) 

V.  (a)  Wires  2  and  3  (parallel) 

(6)  Wires  1,  2,  and  3  (parallel) 

TT 
T,     . 


/Diameter  of  wire  2\2 
\Diameter  of  wire  1 

Resistance  of  iron 


/resistance  of  wire  1 


IreJA 
ire  2/ 


Resistance  of  copper 
IV.  (c)  Rz  +  R3 

V.  (c)l  =  l  +  JLf  .,*  = 


^resistance  of  wire 

resistance  of  German  silver 
resistance  of  copper 

.  ohms ;  joint  resistance  (series),  IV,  (a) 
ohms ;  joint  resistance  (parallel),  V,  (a) 

.ohms;  joint  resistance  (parallel),  V,  (6)  =  ohms. 


.  ohms. 
.  ohms. 


[84] 


EXPERIMENT  32  A 


FIG.  64 


TO  MEASURE  AN  UNKNOWN  RESISTANCE  BY  MEANS  OF  WHEATSTONE'S  BRIDGE  AND 
TO  FIND  HOW  THE  DIAMETER  AND  MATERIAL  OF  A  WIRE  AFFECT  ITS  RESISTANCE 

If  a  current  is  made  to  divide,  as  at  a  (Fig.  64),  so  that  part  of  it  flows  along  the  branch  abc  and 
part  along  the  branch  adc,  then  there  will  be  a  continual  fall  in  potential  in  going  from  a  to  c  over 
each  branch.    Hence  for  any  point  b  in  one  branch  there  must  be  in 
the  other  branch  a  corresponding  point  d  at  which  the  same  potential 
exists.     If  these  two  points  are  connected  through  a  galvanometer 
G,  no  current  will  flow  through  this  galvanometer,  since  the  same 
electrical  pressure  exists  at  b  as  at  d.    If  the  end  of  the  connecting 
wire  is  moved  a  little  to  the  right  of  d,  a  current  will  flow  in  one 
direction  through  G;  while  if  it  is  moved  a  little  to  the  left,  a  cur- 
rent will  flow  through  G  in  the  opposite  direction.    Hence,  in  order 
to  find  experimentally  the  point  d  which  has  the  same  potential  as 
the  point  b,  we  have  only  to  move  the  end  of  the  galvanometer  wire 
along  the  branch  adc  until  we  find  a  point  at  which  the  galvanometer 
shows  no  deflection.    When  this  point  has  been  found,  the  resistance  of  the  four  branches  ad(=  J*) 
dc  (=  $),  ab  (~  R),  and  be  (=  X)  may  be  proved  to  be  related  in  the  following  way: 

z>  I  r\        T>  I  ~v 
Jr/1£  =  Ji/JL. 

To  prove  that  this  is  so,  we  have  only  to  apply  Ohm's  law.  For  if  PZ>1  represents  the  potential 
difference  between  a  and  d,  and  PDZ  that  between  d  and  c,  then,  since  b  and  d  have  the  same  poten- 
tial, PJ)l  will  also  represent  the  potential  difference  between  a  and  b,  and  PDZ  that  between  b  and  c. 
Now  by  Ohm's  law,  since  the  same  current  Cl  is  flowing  through  ad  and  dc,  we  have  Cl  =  PDjP  = 
PDJQ,  or  PDJPDZ  =  P/Q.  Similarly,  on  the  lower  branch,  PDjPD^  =  R/X.  Therefore  P/Q  =  R/X 
and  X=  Q  x  R/P. 

(a)  Stretch  No.  30  German-silver  wire  between  a  and  c,  as  in  Fig.  65,  place  a  meter  stick  beneath 
it,  and  then  connect  a  simple  or  a  dry  cell  B  to  the  terminals  a  and  c.  Between  the  binding  posts  a 
and  b  insert  some  known  resistance,  B 

say  a  1-ohm  coil.  Between  b'  and 
c  insert  a  3-m.  coil  of  No.  30  copper 
wire.  The  brass  strap  between  b  and 
b'  has  a  negligible  resistance,  so  that 
the  whole  of  it  may  be  considered 
as  the  point  b  of  Fig.  64.  Connect  to 
the  binding  post  at  m  one  terminal  of  a  D'Arsonval  galvanometer  G.  This  instrument  is  precisely 
that  shown  in  Fig.  56,  save  that  a  slender  pointer  must  be  inserted  in  the  place  provided  for  it  for 
the  sake  of  making  small  deflections  more  easily  observable. 

Touch  the  free  terminal  of  the  galvanometer  at  a  number  of  points  along  the  wire  ac  until  you 
find  that  point  at  which  the  galvanometer  shows  no  deflection  on  making  contact.  Since  the  wire  etc 
is  uniform,  the  ratio  of  the  resistances  P  and  Q  is  simply  the  ratio  of  the  lengths  ad  (=  ^)  and 
dc  (=  Z2).  Hence, 


or 


=      X 


(6)  In  the  same  way  measure  the  resistance  of  exactly  50  cm.  of  No.  30  iron  wire,  and  by  the  law 
of  lengths  calculate  from  the  result  the  resistance  in  ohms  of  such  a  wire  3  m.  long. 

[85] 


EXPERIMENT  32  A    (Continued) 

(c)  In  the  same  way  measure  the  resistance  of  exactly  25  cm.  of  No.  30  German-silver  wire,  and 
compute  from  the  result  the  resistance  of  such  a  wire  3  m.  long. 

(cT)  Measure,  also,  the  resistance  of  exactly  50  cm.  of  No.  24  German-silver  wire,  and  compute 
from  the  result  the  resistance  of  such  a  wire  3  m.  long. 

Questions,  a.  The  resistance  of  an  iron  wire  is  how  many  times  that  of  a  copper  wire  of  the  same  diame- 
ter and  length  ? 

b.  The  resistance  of  a  German-silver  wire  is  how  many  times  that  of  a  copper  wire  of  the  same  length  ? 

c.  The  diameter  of  No.  24  wire  is  twice  that  of  No.  30  wire  (see  Appendix  B).   How  does  the  resistance 
of  a  wire  depend  upon  its  diameter  ? 


RECORD  OF   EXPERIMENT 


/,  IN  CENTIMETERS 

/s  IN  CENTIMETERS 

R  IN  OHMS 

X  IN  OHMS 

ItESISTANCE  OF  300  CM. 

(«) 

(») 

(<0 

(<0 

Resistance  of  iron 
Resistance  of  copper 

/Diameter  of  No.  24  wire\2 
\Diameter  of  No.  30  wire/ 


resistance  of  German  silver 
resistance  of  copper 

resistance  of  300  cm.  of  No.  30  German-silver  wire 
'  resistance  of  300  cm.  of  No.  24  German-silver  wire 


[86] 


EXPERIMENT  33 

HOW  DOES  THE  RESISTANCE  OF  GALVANIC  CELLS  DEPEND  .UPON  THE  AREA  OF  THE 
PLATES   IMMERSED,   THE   DISTANCE  BETWEEN  THE   PLATES,  AND   THE  METHOD   OF 

CONNECTING  THEM? 

I.  Area  of  plates  immersed,   (a)  Connect  an  improvised  Daniell  cell  *  to  the  single  turn  of  coarse 
copper  wire  of  the  galvanoscope  or  to  an  ammeter.    Record  the  reading  of  the  instrument  used. 

(6)  Lift  the  plates  gradually  out  of  the  glass  and  record  the  effect.  Since,  as  proved  in  Exp.  31, 
the  E.M.F.  is  not  diminished  by  decreasing  the  area  of  the  plates  immersed,  what  do  you  conclude, 
from  Ohm's  law,  must  have  changed  in  the  circuit  as  the  plates  were  lifted  ?  How,  then,  is  the  internal 
resistance  affected  by  the  size  of  the  plates  ? 

For  a  battery  circuit  Ohm's  law  must  then  be 

€=  E.M.F. 

where  Re  is  the  resistance  of  the  circuit  external  to  the  battery, -and  R.  is  the  internal  resistance 
of  the  battery. 

II.  Distance  between  plates.    Dispense  with  the  plate  holder  of  the  cell.    Press  the  wires  firmly 
against  the  plates  and  record  the  reading  of  the  instrument  used,  first,  when  the  plates  of  the  cell  are 
brought  as  close  together  as  possible,  that  is,  on  adjacent  sides  of  the  porous  cup,  and  second,  when 
the  plates  are  held  as  far  apart  as  possible  in  the  cell.    How  is  Rt  affected  by  the  distance  between 
the  plates  ? 

III.  Internal  resistance  of  cells  in  series,    (a)  Connect  a  single  Daniell  cell  to  the  single  turn  coil 
of  the  galvanoscope  or  to  an  ammeter.    (In  this  and  succeeding  parts  of  the  experiment,  if  the  gal- 
vanoscope is  used,  the  compass  should  be  slipped  along  in  the  frame  until  the  deflection  at  first  is  not 

lore  than  16°.)    The  external  resistance  of  the  circuit  is  now  very  small  and,  without  appreciable 

E.M.F. 

jrror,  may  be  considered  equal  to  zero,  so  that  under  these  conditions  C  =  — '-  • 

Now  introduce  enough  German-silver  wire  in  series  with  the  circuit  to  reduce  the  current 
'ammeter  reading  or  deflection,  depending  on  the  instrument  used)  to  one.  half  its  former  value, 
[easure  the  length,  in  centimeters,  of  the  German-silver  wire  thus  introduced  and  find  its  resistance 
in  ohms.  (1  cm.  of  No.  30  German-silver  wire  has  a  resistance  of  .0621  ohms.) 

Since  the  introduction  of  the  German-silver  wire  halved  the  current,  the  resistance  of  the  circuit 

•p  -\ t  -p 
must  have  been  doubled.    Hence,  by  the  equation  C  =  — — '—^ ,  the  resistance  Re  of  the  German-silver 


rire  introduced  into  the  circuit  must  be  equal  to  the  internal  resistance  Rt  of  the  cell.  Call  this 
resistance  (R^)^ 

(5)  In  the  same  way  find  the  internal  resistance  of  a  second  Daniell  cell,  expressed  first  in  centi- 
meters of  No.  30  German-silver  wire  and  then  in  ohms.  Call  this  resistance  (-R,-)2- 

(<?)  By  the  same  method  find  the  combined  internal  resistance  of  the  two  cells  joined  in  series. 
Call  this  resistance  Rs. 

(cT)  How  does  Rt  compare  with  the  sum  of  (R^^  and 


*  For  these  cells  use  a  saturated  solution  of  copper  sulphate  outside  the  porous  cup  and  a  10%  solution  of  sulphuric  acid 
inside  the  porous  cup. 

At  the  close  of  the  day's  work  place  the  porous  cups  in  a  battery  jar,  cover  with  water,  and  add  from  5  to  10%  as  much 
nitric  acid  as  there  is  water.  The  nitric  acid  is  to  remove  the  copper  deposited  in  the  pores  of  the  cup.  The  internal  resistance 
of  cells  when  made  as  above  will  seldom  be  more  than  4  ohms  and  often  less  than  1  ohm. 

[87] 


EXPERIMENT  33    (Continued) 

IV.  Internal  resistance  of  cells  in  parallel,    (a)  By  the  above  method  find  the  joint  internal  resist- 
ance of  the  two  cells  connected  in  parallel.    Call  their  joint  resistance  in  parallel  RP. 

(6)  Compare  RP  as  thus  obtained  with  Rp  as  computed  by  the  formula  for  resistances  in  parallel ; 

111  CK,.),  x 

—  — ' or     RP  =  ^—5^1 — 


Questions,    a.  Why  is  the  carbon  in  a  dry  cell  made  about  an  inch  in  diameter  rather  than  the  size  of  a 
lead  pencil  ? 

b.  Commercial  storage  batteries  are  made  with  large  plates  placed  close  together.    Would  you  expect 
their  internal  resistance  to  be  large  or  small  ?    Why  ? 

c.  If  n  cells  each  having  the  same  internal  resistance  R{  were  connected  in  series,  what  would  be  their 
joint  internal  resistance  ? 

d.  If  the  n  cells  were  connected  in  parallel,  what  would  be  their  joint  internal  resistance  ? 

e.  How  should  cells  be  connected  in  order  to  get  as  large  a  current  as  possible,  if  the  external  resistance 
is  small  ?  if  the  external  resistance  is  large  ? 


RECORD  OF  EXPERIMENT 

I.  (a)  Deflection  of  compass  for  large  plates  = ,  (i)  for  small  plates  = 

or  (a)  Ammeter  reading  for  large  plates         =  ,  (b)  for  small  plates  =3 

II.  (a)  Deflection  of  compass,  plates  close        = ,  (Z*)  plates  far  apart  = 

or  (a)  Ammeter  reading,  plates  close  =  ,  (6)  plates  far  apart  = 


Ri  IN  CENTIMETERS  OF  No.  30 
GERMAN-SILVER  WIRE 

INTERNAL,  RESISTANCE  IN  OHMS 

III.  (a)  Cell  1 

(6)  Cell  2 

(c)  Cells  1  and  2  in  series 

IV.  («)  Cells  1  and  2  in  parallel 

III.    (d)   (fl,)l  +  (#£),  = 


IV.  (6) 


..).     X     (/?;),    _ 


ohms ;  joint  resistance  in  series,  III,  (c)      = ohms. 

ohms;  joint  resistance  in  parallel,  IV,  (a)  =  ohms. 


[88] 


EXPERIMENT  34 


WHICH    WOULD   YOU    INSTALL   IN   YOUR   HOME,   TUNGSTEN   LAMPS   OR   CARBON- 
FILAMENT  LAMPS?   WOULD  YOU  CONNECT  THEM  IN  SERIES  OR  IN  PARALLEL? 

In  answering  the  first  question  one  must  take  into  consideration  the  initial  cost,  the  cost  of  main- 
tenance, and  the  cost  of  Dperation  of  the  lamps.  The  initial  cost  of  tungsten  lamps  (Mazda  lamps) 
is  somewhat  more  than  the  initial  cost  of  the  ordinary  carbon-filament  lamps.  This  extra  cost  of  tung 
sten  lamps  must  then  be  at  least  offset  by  a  lower  cost  of  operation  if  tungsten  lamps  are  to  be  chosen. 

I.  Comparison    of    cost    of 
operation.    Connect  four  lamps 
in  parallel  as  in  Fig.  66.  Intro- 
duce an  ammeter  hi  series  in  the 
"  line"  and  connect  a  voltmeter 
across  the  line. 

Caution.  Do  not  turn  on 
the  current  until  an  instructor 
has  O.K.'d  your  electrical  con- 
nections. A  mistake  might 
completely  ruin  an  electrical 
instrument. 

Lamps  a  and  b  are  tungsten 
lamps  whose  ratings  are  about 
20  watts  and  40  watts  respec- 
tively. Lamps  e  and  d  are  or- 
linary  carbon-filament  lamps 
e  ratings  are  about  55 
watts  and  100  watts  respec- 
tively. If  the  candle  powers  of 
the  lamps  are  not  marked  on 
them,  consult  the  instructor. 

Turn  on  lamp  a.  Record  the 
voltmeter  and  ammeter  read- 
ings. From  these  readings  com- 
pute the  number  of  watts  re- 
quired to  operate  the  lamp,  and  compare  with  the  voltage  marked  upon  it.  Watts  =  volts  x  amperes. 
Calculate  also  the  number  of  watts  required  to  produce  one  candle  power. 

Turn  off  lamp  a  and  turn  on  lamp  b  and  then  make  a  similar  set  of  observations  and  calculations 
for  lamp  b. 

Make  similar  tests  with  lamps  c  and  d. 

Compute  with  the  aid  of  Ohm's  law  the  resistance,  when  hot,  of  each  of  the  lamps  a,  6,  G-,  and  d 
id  call  these  resistances  R^  RZ,  ES,  and  R^  respectively.    Do  not  record  more  than  three  significant 
igures  in  these  results. 

II.  How  to  connect  lamps  in  a  lighting  circuit,    (a)  Turn  on  all  the  lamps  as  you  now  have  them 
connected  (that  is,  in  parallel,  as  in  Fig.  66).    Record  the  readings  of  the  voltmeter  and  the  ammeter 

id  from  these  readings  compute  the  joint  resistance,  when  hot,  of  the  four  lamps  in  parallel.    Call 
their  joint  resistance  RP. 

[891 


FIG. 


EXPERIMENT  34   (Continued) 

Compute  jRP  also  by  use  of  the  equation*  -  -  H h  -  -  H 

RP     R^      R_2      R&     Rt 

Compare  the  two  values  of  RP  obtained  above. 

(6)  Now  connect  the  four  lamps  in  series  with  the  ammeter  as  in  Fig.  67  and  record  its  reading. 
Then  record  the  voltmeter  reading  when  connected  successively  across  each  individual  lamp,  and  also 
when  connected  across  all  four  lamps. 

Again  compute  the  resistance  of  each  lamp  under  these  conditions ;  that  is,  when  the  lamp 
filaments  are  much  colder. 

Also  compute  the  resistance  Rs  of  the  four  lamps  in  series,  first  from  the  voltmeter  and  ammeter 
.readings  and  then  by  use  of  the  equation  for  resistances  in  series,  that  is,  Rs  =  R^  +  R2  +  Its  +  _R4. 


FIG.  67 


Questions,  a.  The  life  of  either  the  tungsten  or  the  carbon-filament  lamp  is  from  1000  to  2000  hr. 
Allowing  for  breakages,  assume  that  their  life  is  500  hr.  At  the  price  charged  by  your  local  power  plant  per 
kilowatt  hour  for  electricity  what  would  it  cost  to  operate  one  16-candle-power  tungsten  lamp  (Mazda)  for 
the  500  hr.  What  would  it  cost  to  operate  one  carbon-filament  lamp  of  the  same  candle  power  for  the  same 
length  of  time  ?  What  then  is  the  saving  in  the  cost  of  operation  of  one  lamp  during  its  life  (assumed 
to  be  500  hr.)  ? 

b.  Is  the  extra  initial  cost  of  tungsten  lamps  more  than  offset  by  a  lower  cost  of  operation  ?    If  so, 
how  much  ?    (Before  answering  this  question  ask  your  dealer  to  quote  you  prices  on  Mazda  lamps  and 
also  on  ordinary  carbon-filament  lamps  of  say  16  candle  power  in  each  case.) 

c.  Is  the  resistance  of  a  carbon  filament  increased  or  decreased  by  increasing  its  temperature  ? 

d.  How  is  the  resistance  of  tungsten  affected  by  increasing  its  temperature  ? 

e.  Make  a  diagram  of  the  connections  for  lighting  three  rooms  of  a  house  with  four  lamps  in  each  room. 

*  The  following  is  a  practical  way  of  solving  a  similar  equation.  If,  for  example,  four  lamps  have  resistances  of  220, 
109,  605,  and  297  ohms  respectively,  their  joint  resistance,  Rp,  when  connected  in  parallel,  is  given  by 


—  +  — 

220      109 


1    1 
605   297 
=  .00455  +  .00917  +  .00166  +  .00336 
=  .01874. 

= '• —  =  53.4  ohms. 

.01874 


[90] 


EXPERIMENT  34  (Continued) 
RECORD  OF   EXPERIMENT 


LAMP 

VOLTS 

AMPKRES 

WATTS 

CANDLE  POWER 

WATTS  PER 
CANDLE  POWER 

RESISTANCE 

(WHEN  HOT) 

„ 

- 

Ri  ~ 

<•> 

R2  = 

00 

Rs  = 

00 

Rt  = 

(a),  (6),  (c),  and  (rf), 
in  parallel 

* 

* 

* 

RP  = 

II. 


LAMP 

VOLTS 

AMPERES 

RESISTANCE 
(WHEN  COLDER) 

(a) 

R^ 

(») 

«,= 

(«) 

«,= 

09 

«4  = 

(a),  (6),  (c),  and  (d), 
in  series 

p    

t  j          L        j. 

,  from  — -  =  —  +  --  +  —  +  — , 

H        K        /i        K        /t 


RP,  from  I, 


(For  above,  use  values  of  7?x ,  J?2,  etc., 
when  hot.) 

7?5,  from  Rs=Rl  +  R2  +  Ra  +  Rv 


Rs,  from  II,  =  

(For  above,  use  values  of  Rlt  Rz,  etc., 
when  colder.) 


.ohms 
ohtus 


These  spaces  to  be  left  blank  by  the  student. 


[91] 


EXPERIMENT  34  A 


HEATING  EFFECTS  OF  THE  ELECTEIC  CURRENT 

The  application  of  electric  currents  to  heating  is  daily  becoming  of  greater  commercial  importance. 
Our  highest  temperatures  are  obtained  in  the  electric  arc  and  the  electric  furnace.  Electric  disk  stoves, 
teakettles,  egg  cookers,  toasters,  chafing  dishes,  percolators,  grills,  water  heaters,  immersion  coils,  flat- 
irons,  curling  irons,  mangles,  foot  warmers,  radiators,  shaving  mugs,  milk  warmers,  and  sterilizers  are 
some  of  the  household  conveniences.  Electric  soldering  pots,  soldering  irons,  glue  cookers,  glue  pots 


To  Line 


FIG.  68 


FIG. 


FIG    70 


for  cabinet  makers,  melting  pots  for  lead  alloys,  instantaneous  heaters  for  soda  fountains,  mangles, 
fluting  irons,  automobile  tire  vulcanizers,  and  electric  welders  are  also  some  of  the  commercial  applica- 
tions of  heating  by  the  electric  current. 

The  designer  and  the  producer  of  these  useful  appliances  are  interested  in  increasing  the  percentage 
of  the  energy  of  the  electric  current  which  is  transformed  into  heat  available  for  the  intended  purpose. 
The  ratio  of  this  available  heat  energy  (or  output)  to  the  electric  energy  (or  input)  for  any  of  these 
levices  is  its  efficiency. 

The  consumer  or  user  of  these  appliances  is  interested  not  only  in  their  efficiency  and  cost  of 
jration  but  also  in  their  convenience. 

Heating  water  with  the  electric  current.  Pour  1  Ib.  of  cold  water  into  the  teakettle  used  in 
Jxp.  18  and  place  it  on  the  electric  disk  heater  of  Fig.  68.  Connect  an  ammeter  in  series  with  the 
heater  and  line  and  a  voltmeter  across  the  line,  as  in  Fig.  71. 


To  healer 


^ 

Line 


FIG.  71 

Caution.  Do  not  turn  on  the  current  until  an  instructor  has  O.K.'d  the  arrangement  of  your  apparatus 
Now  turn  on  the  current  and  simultaneously  observe  the  exact  time  that  it  is  turned  on. 
Record  the  voltmeter  and  the  ammeter  readings  every  minute  until  the  water  boils.    Then  turn  off 
the  current,  noting  the  exact  time  that  it  is  turned  off. 

f931 


EXPERIMENT  34  A    (Continued) 

From  the  average  voltmeter  and  ammeter  readings  and  from  the  time  compute  the  number  of 
kilowatt  hours  of  electricity  used. 

At  the  local  price  per  kilowatt  hour  for  electricity,  compute  the  cost  of  heating  1  qt.  of  water  to 
the  boiling  point. 

Compare  this  cost  to  the  cost  of  heating  1  qt.  of  water  to  the  boiling  point  with  the  gas  stove 
(see  Exp.  18  A). 

Practical  efficiency  of  the  electric  heater.  Pour  500  g.  of  water  at  a  temperature  of  12°  C.  or  15°  C. 
below  room  temperature  into  the  teakettle  and  place  a  thermometer  in  the  water. 

Turn  on  the  current ;  stir  the  water  continually  with  the  thermometer ;  observe  the  exact  time 
when  the  water  attains  a  temperature  which  is  10°  C.  below  room  temperature  ;  and  again  observe  the 
time  when  the  water  attains  a  temperature  which  is  10°  C.  above  room  temperature. 

The  practical  efficiency  is  then  the  ratio  of  the  number  of  calories  of  heat  received  by  the  water  to 
the  number  of  calories  of  heat  produced  by  the  heating  effect  of  the  electric  current  in  the  coils  of  the 

stove ;  that  is,  •  ,  ,     c 

^      ,.    ,     ~?  •  weight  ot  water  X  change  in  temperature 

Practical  efficiency  =  —  —  • 

.24  x  watts  x  seconds 

Questions,  a.  If  the  teakettle  were  covered  with  asbestos,  would  the  combined  efficiency  of  the  stove  and 
teakettle  be  higher  ?  Why  ? 

b.  If  the  electric  teakettle  of  Fig.  69  is  used,  should  its  efficiency  be  higher  than  that  of  a  teakettle  used 
with  the  electric  disk  stove  of  Fig.  68  ?   Why  ?   (The  teakettle  of  Fig.  69  has  a  "  self-contained  heating  coil.") 

c.  How  would  you  expect  the  efficiency  of  the  immersion  heater  shown  in  Fig  70  to  compare  with  the 
efficiency  of  either  of  the  other  heaters  shown  ?  Give  reason  for  your  answer. 

d.  In  obtaining  the  "  theoretical  efficiency  "  the  water  equivalent  of  the  teakettle  would  have  to  be  taken 
into  account.    Would  the  "  theoretical  efficiency  "  be  higher  or  lower  than  the  "  practical  efficiency  "  ? 


EXPERIMENT  35 


ELECTROLYSIS  AND  THE  STORAGE  BATTERY 

I.  Electrolysis  of  water.    Bare  the  ends  of  two  pieces  of  copper  wire  and  wrap  each  about  the 
head  of  a  wire  nail.*    Connect  the  other  ends  of  the  wires  to  the  terminals  of  two  dry  cells  joined 
in  series.    Dip  the  ends  of  the  nails  into  a  dilute  solution  of  sulphuric  acid  like  that  used  in  Exp.  28. 
Is  the  nail  from  which  the  bubbles  appear  first  and  most  abundantly  connected  to  the  +  or  to  the  — 
pole  of  the  battery ;  that  is,  to  the  carbon  or  to  the  zinc  ?    This  gas  which  is  given  off  most  abun- 
dantly is  hydrogen ;  that  which  appears  at  the  other  nail  is  oxygen.    In  order  to  account  for  these 
effects  we  assume  that  when  the  molecules  of  sulphuric  acid  (H2SO4)  go  into  solution  in  water  they 
split  up  into  two  electrically  charged  atoms,  or  ions,  of  hydrogen  and  one  oppositely  charged  ion  of 
SO4.    It  was  this  hydrogen  which,  according  to  this  hypothesis,  appeared  at  one  nail  while  the  SO4 
went  to  the  other  and  there  gave  up  an  atom  of  oxygen.    If  this  hypothesis  is  correct,  must  the 
hydrogen  ion  in  solution  carry  a  +  or  a  —  charge  in  order  to  appear  upon  the  nail  upon  which  you 
observed  it  ?    What  kind  of  a  charge  must  the  SO4  ion  carry  ? 

II.  Electroplating.      Remove   the   nails   and  attach  each  bare  wire  to  some  sort  of  improvised 
metal  clip  (ordinary  paper  fasteners  are  excellent).    In  each  of  these  clips  place  a  nickel  and  dip  the 
lower  half  of  each  into  a  solution  of  copper  sulphate  (CuSO4).    About  which  nickel  do  you  now  see 
bubbles,  the  one  connected  to  the  +  or  the  one  connected  to  the  —  pole  of  the  battery  ?    (The  former 
is  called  the  anode,  the  latter  the  cathode.)    These  bubbles  are  oxygen.    After  about  a  minute  remove 
the  nickels  and  dry  them  with  a  cloth.     Record  what  has  happened.     Decide  from  your  results 
whether  the  copper  ions  of  the  copper  sulphate  solution  carry  +  or  —  charges. 

Interchange  the  nickels  between  the  two  clips  and  repeat  the  above  operations.  Record  the  results. 
(If  you  wish  to  restore  your  nickels  quickly  to  their  original  condition,  dip  them  for  an  instant  in 
strong  nitric  acid  and  rub  with  an  old  cloth.) 

Ill  (a).  The  storage  battery,  f  Arrange  a  simple  cell  in  the  manner  shown  in  Fig.  72,  a  and  b 
nng  the  copper  and  the  zinc  strip  to  which  are  connected  the  terminals  of  an  improvised  voltmeter 
consisting  of  the  1000-ohm  resistance  coil  E  and  the  galvanoscope  V,  with  the  compass  beneath  its 
high-resistance  coil.  A  is  an  improvised  ammeter  consisting  of  an- 
other galvanoscope  with  the  compass  beneath  the  25-turn  coil  of 
coarse  wire ;  r  is  a  resistance  of  about  100  ohms  (use  for  it  4  m.  of 
No.  36  German-silver  wire,  wound  on  a  spool  of  insulated  wire  or 
held  0:1  the  frame  of  Fig.  G3  if  bare  wire)  ;  B  is  a  battery  of  two 
dry  cells  connected  in  series  but  not  joined,  at  first,  to  the  ter- 
minals m  and  n  of  the  cell  circuit.  Move  the  compass  of  V  until 
the  deflection  is  8°  or  10°.  This  amount  of  deflection  then  rep- 
resents the  E.M.F.  of  a  copper-zinc  sulphuric  acid  cell  (approxi- 
mately 1  volt). 

Now  replace  the  zinc  and  the  copper  strip  by  two  strips  of  sheet  lead.  Does  the  voltmeter  Fnow 
indicate  any  E.M.F.  ?  Explain  the  reason.  Next  connect  m  and  n  to  the  terminals  of  the  dry  battery 
#,  and  as  soon  as  the  needles  are  sufficiently  quiet,  record  the  deflections  shown  by  both  A  and  V\ 
then  watch  both  needles  carefully  for  about  two  minutes  and  record  the  readings,  expressing  the 
reading  of  A  simply  in  scale  divisions,  but  that  of  V  in  both  scale  divisions  and  volts. 

*  Platinum  electrodes  are  better,  but  they  are  less  convenient  and  much  more  expensive. 

t  Two  sets  of  students  are  expected  to  work  together  on  this  experiment,  and  where  low-reading  voltmeters  and  ammeters 
are  available,  the  method  of  III  (b)  will  be  found  somewhat  shorter  than  that  of  III  (a)  and  just  as  satisfactory. 

[95] 


B  ~ 


FIG.  72 


EXPERIMENT  35   (Continued) 

Now  short-circuit  the  terminals  o  and  s  of  the  resistance  r  by  pressing  a  strip  of  metal  against  the 
two  binding  posts  o  and  s  or  by  connecting  them  with  a  copper  wire.  Watch  the  plates  and  note 
the  hydrogen  appearing  in  considerable  quantity  about  the  cathode,  while  but  little  oxygen  appears 
about  the  anode.  After  the  current  has  been  running  through  the  short  circuit  on  r  for  about  two 
minutes  lift  the  plates  from  the  liquid.  Do  you  see  a  faint  reddish  deposit  upon  the  anode  where  the 
oxygen  would  naturally  have  appeared  ?  If  not,  let  the  current  run  a  little  longer  and  observe  again. 
This  deposit  is  lead  peroxide  (PbO2).  Why,  then,  did  so  little  oxygen  gas  appear  about  the  anode  ? 

Replace  the  plates  in  the  acid,  take  away  the  shunt  from  os,  and  record  the  reading  of  V.  By  how 
many  volts  is  it  now  larger  than  it  was  when  m  and  n  were  first  joined  to  j5  ?  Disconnect  m  and  n 
from  B  and  observe  how  many  volts  of  E.M.F.  have  been  developed  between  the  lead  plates.  Now 
watch  the  ammeter  as  you  join  m  and  n  to  each  other.  What  is  the  direction  of  the  observed  cur- 
rent with  reference  to  that  which  the  battery  sent  through  the  ammeter?  Watch  the  voltmeter  and 
the  ammeter  for  two  minutes  while  the  tstoraye  cell  is  discharging.  In  view  of  this  back  E.M.F.  which 
the  experiment  has  shown  was  developed  in  the  lead  cell  by  the  deposit  of  lead  peroxide  on  the  anode, 
explain  why,  during  the  charging  of  the  storage  cell,  the  voltmeter  deflection  rose,  while  that  of  the 
ammeter  fell.  From  your  experiment  decide  how  many  volts  are  required  to  charge  a  storage  cell.* 

Ill  (&).  The  storage  battery.  Make  a  cell  like  that  shown  in  Fig.  73,  with  two  well-cleaned  lead 
plates  dipped  into  a  solution  made  of  one  part  sulphuric  acid  to  ten  parts  water. 

Connect  a  voltmeter  across  the  cell  and  see  if  it  produces  any  E.M.F. 

To  charge  the  cell  connect  it  in  series  with  a  resistance  of  about  5  or  6  ohms  (about  1  m.  of 
No.  30  German-silver  wire),  a  low-reading  ammeter,  and  two  dry  cells.  At  the  same  instant  in  which 
the  last  connection  of  the  charging  circuit  is  made,  one 
student  should  record  the  voltmeter  reading  and  another 
the  ammeter  reading.  Record  the  reading  of  each  meter 
every  ten  or  fifteen  seconds  for  two  minutes. 

Now  increase  the  charging  current  by  connecting  the 
ends  of  a  meter  of  No.  24  copper  wire  to  the  binding  posts 
which  hold  the  German-silver  wire.  Watch  the  plates  and 
note  the  hydrogen  appearing  in  considerable  quantity  about 
the  cathode,  while  but  little  oxygen  appears  about  the  anode. 
After  the  increased  charging  current  has  been  running  for 

about  two  minutes  lift  the  plates  from  the  liquid.  Do  you  see  a  faint  reddish  deposit  upon  the  anode 
where  the  oxygen  would  naturally  have  appeared?  If  not,  let  the  current  run  a  little  longer.  This 
deposit  is  lead  peroxide  (PbO2).  Why,  then,  did  so  little  oxygen  appear  about  the  anode? 

Replace  the  plates  in  the  acid,  take  away  the  copper  wire  which  was  shunted  across  the  German- 
silver  wire,  and  record  the  voltmeter  reading.  By  how  many  volts  is  it  now  larger  than  it  was  when 
m  and  n  were  first  joined  to  If?  Disconnect  m  and  n  from  B  and  observe  how  many  volts  of  E.M.F. 
have  been  developed  between  the  lead  plates.  Now  watch  the  ammeter  as  you  join  m  and  n  to  each 
other.  What  is  the  direction  of  the  observed  current  with  reference  to  that  which  the  battery  sent 
through  the  ammeter  ?  Watch  the  voltmeter  and  the  ammeter  for  two  minutes  while  the  storage  cell 
is  discharging.  In  view  of  this  back  E.M.F.  which  the  experiment  has  shown  was  developed  in  the  lead 
cell  by  the  deposit  of  lead  peroxide  on  the  anode,  explain  why,  during  the  charging  of  the  storage  cell, 
the  voltmeter  deflection  rose,  while  that  of  the  ammeter  fell.  From  your  experiment  decide  how 
many  volts  are  required  to  charge  a  storage  cell. 

*  If  you  wish  to  repeat  the  experiment  with  the  same  lead  plates,  clean  them  first  very  thoroughly  with  sandpaper. 


FIG.  73 


[96] 


EXPERIMENT  36 


INDUCED  CURRENTS 

I.  Induction  of  currents  by  magnets,  (a)  Set  up  the  D'Arsonval  galvanometer  (Fig.  74)  and 
insert  in  the  place  provided  for  it  a  slender  wire  or  broom-corn  pointer  in  the  manner  shown  in  the 
figure.  Short-circuit  a  simple  cell  by  means  of  a  few  feet  of  copper  wire ;  then  to  the  galvanometer 
terminals  touch  wires  which  are  connected  to  the  cell  and  note 
the  direction  of  deflection.  (The  object  of  the  short-circuiting  is 
to  prevent  a  too  violent  throw  of  the  coil.)  Record  the  terminal 
(right  or  left)  of  the  galvanometer  at  which  the  current  entered 
it  when  the  deflection  was  in  a  given  direction  (right  or  left). 
This  will  enable  you  henceforth  to  know  at  which  terminal  any 
current  enters  your  galvanometer,  as  soon  as  you  observe  the 
direction  of  deflection.  Connect  to  the  galvanometer  a  600-  or 
700-turn  coil  A  of  No.  27  copper  wire.  Take  particular  pains  to 
scrape  the  ends  of  all  wires  which  are  to  be  joined,  and  to  twist 
the  scraped  ends  firmly  together. 

Thrust  the  coil  A  suddenly  over  the  north  pole  of  the  bar  magnet  and  note  and  record  the 
direction  and  the  approximate  amount  of  the  deflection  of  the  end  of  the  pointer  attached 
to  the  coil.  A  paper  scale  supported  between  the  walls  beneath  the  pointer  will  enable  you  to 
estimate  amounts. 

(5)  From  the  direction  of  the  deflection  determine  the  direction  of  the  current  induced  in  the 
coil  of  wire  thrust  over  the  pole.  While  this  induced  current  was  flowing,  did  it  make  the  end  of  the 
coil  —  considered  as  a  temporary  magnet  (see  Exp.  30)  —  which  was  approaching  the  N  pole,  an  jV 
an  S  pole  ? 

(c)  Suddenly  withdraw  the  coil  from  the  magnet.  Note  and  record  as  before  the  direction  and 
lount  of  deflection.  How  does  the  direction  and  amount  of  the  induced  current  now  compare  with 
that  found  in  (a)  ?  Is  the  end  of  the  coil  which  leaves  the  magnet  last  of  the  same  sign  as  the  pole 
of  the  magnet  or  of  unlike  sign  ? 


Us 


(d)  Draw  in  your  notebook  four  figures  like  those  shown  in  Fig.  75  and  insert  in  each  the  signs 
the  poles  of  the  coil  due  to  the  induced  current,  when  the  coil  is  in  the  four  positions  indicated  in 

e  figures  and  moving  in  the  directions  indicated  by  the  arrows. 

(e)  Repeat  the  same  experiments  with  the  S  pole  of  the  magnet  and  observe  in  each  case  the 
lirection  of  deflection  and  the  direction  of  the  current  induced  in  the  coil.    Is  the  nature  of  the 

iduced  magnetism  of  the  coil  A  in  every  case  such  as  to  oppose  or  to  assist  the  motion  of  the  coil  V 

[97] 


EXPERIMENT  36    (Continued) 


II.  Induction  of  currents  by  electromagnets,    (a)  Slip  the  700-turn  coil  used  in  I  over  an  iron 
bar  (for  example,  one  of  the  tripod  rods)  and  connect  it  through  a  commutator  with  a  battery  B  of 
one  or  two  dry  cells,  in  the  manner  shown  in  Fig.  76.    Place  a  second  similar  coil  over  this  bar  and 
connect  it  with  the  D'Arsonval  galvanometer,  as  shown.    Now  make  the  circuit  by  inserting  the  upper 
part  of  the  commutator,  and  record  the  effect  produced  upon  the  needle.    From  the  direction  of 
deflection  of  the  pointer,  find  the  direction  in  which  the  current  flowed  around  the  iron  core  in  the 
coil  attached  to  the  galvanometer  (the  so-called  secondary*).    Was  the  induced  current  in  the  same  or 
in  the  opposite  direction  to  that  in  which  the  current  from  the  cell  is  circulating  around  the  core  in 
the  primary  ?    What  connection  do  you  find  between  this  experiment  and  I  ? 

(6)  Remove  the  commutator  top  and  thus  break  the  circuit  in  the  primary.  Note  the  direction 
and  amount  of  deflection  and  compare  with  that  observed  when  the  current  was  made.  Compare  the 
direction  of  the  induced  current  in  the  secondary  with  that  which  was  flowing  in  the  primary.  Ls  the 
current  in  the  secondary  circuit  produced  by  the  magnetism  of  the 
electromagnet  or  by  changes  in  the  magnetism  of  the  electromagnet? 
Do  the  induced  currents  in  every  case  tend  to  assist  or  to  oppose 
the  changes  which  are  taking  place  in  the  magnetism  of  the  core  ? 

(c)  Push  up  the  base  of  the  tripod  into  contact  with  the  rod 
(Fig.  76),  so  that  the  magnetic  lines  can  have  a  return  iron  path 
instead  of  a  return  air  path.  Observe  the  amount  of  the  deflection  at 
make  or  break  and  compare  with  the  amount  when  the  tripod  base  is 
removed.  (The  difference  will  not  be  large,  but  it  will  be  easily 
observable.) 

III.  Principles  of  the  dynamo  and  the  motor,    (a)  Hold  the  coil  A 
between  the  poles  of  a  horseshoe  magnet  (Fig.  77),  and  in  such  a 

position  that  its  plane  is  perpendicular  to  a  line  joining  the  poles.  Rotate  quickly  through  90°  ; 
that  is,  to  a  position  in  which  its  plane  is  parallel  to  the  lines  of  force.  Observe  the  direction  of 
deflection  of  the  suspended  coil. 

(i)  After  the  pointer  has  come  to  rest,  rotate  the  coil  A  90°  mere  and  note  and  record  the  direc- 
tion of  deflection. 

(c)  Similarly,  rotate  the  -coil  through  the  next  two  quadrants. 

(d)  If  the  coil  were  to  be  rotated  continuously  in  this  way,  what  portions  of  the  rotation  would 
produce  a  current  in  one  direction  and  what  in  the  opposite  direction  ?    In  what  position  of  the  coil 
will  the  induced  current  change  from  one  direction  to  the  other  ? 

(e)  In  a  dynamo  a  coil  is  forced  to  rotate  in  the  strong  field  of  an  electromagnet,  and  induced 
currents  are  produced.    In  a  motor,  currents  are  sent  through  a  coil  which  is  in  a  strong  magnetic 
field,  and  the  coil  is  forced  to  rotate.    Point  out  the  parts  of  the  above  apparatus  which  correspond  to 
the  dynamo  and  those  which  correspond  to  the  motor. 


FIG.  77 


[98J 


EXPERIMENT  37 
TO  DETERMINE  THE  POWER  AND  EFFICIENCY  OF  AN  ELECTRIC  MOTOR 

Connect  the  ammeter  in  series  with  the  motor  to  measure  the  current  through  the  motor,  and  the 
voltmeter  in  parallel  with  it  to  measure  the  P.D.  across  the  motor  (see  Fig.  78). 

For  measuring  the  output  of  small  motors  having  a  grooved  belt  wheel,  use  the  modification  of 
the  Prony  brake  shown  at  the  right  in  Fig.  78. 

Disconnect  the  brake  belt  to  relieve  the  motor  of  its  load.  Close  the  switch  and  slowly  move  the 
lever  of  the  starting  resistance,  or  of  the  rheostat,  so  as  to  cut  out  the  resistance  in  series  with  the  motor. 


w 


Modification  of  Prony  Brake 


FIG.  78 

Now  attach  the  brake  belt  and  increase  the  tension  on  it  by  raising  the  balance  support  until  the 
speed  is  about  100  to  200  II. P.M.  (revolutions  per  minute).  In  the  modified  form  of  Prony  brake 
this  is  accomplished  by  increasing  the  weight  W. 

Let  one  student  read  the  voltmeter  and  ammeter,  another  the  speed  indicator  and.  stop  watch, 
and  another  the  balances. 

The  recorded  voltmeter,  ammeter,  and  balance  readings  should  be  the  mean  of  several  observa- 
tions made  during  the  same  time  that  the  number  of  revolutions  for  one  minute  are  observed. 

Stop  the  motor  by  opening  the  switch.  Wrap  a  thread  several  times  around  the  belt  wheel  and  from 
the  length  of  the  thread  and  the  number  of  turns  determine  the  circumference  of  the  wheel  in  feet. 

The  circumference  in  feet  multiplied  by  the  pull  on  the  belt  in  pounds  (pull  on  the  belt  = 
difference  in  the  two  balance  readings,  or  else  the  single  balance  reading  minus  the  weight)  gives 
the  number  of  foot  pounds  of  work  done  by  the  motor  in  one  revolution.  This  number  of  foot  pounds 
per  revolution  multiplied  by  the  R.P.M.  gives  the  output  of  the  motor  in  foot  pounds  per  minute. 

Express  the  output  in  horse  power,  remembering  that  33,000  ft.  Ib.  per  minute  =  1  horse  power. 

The  input,  or  the  rate  at  which  energy  is  supplied  to  the  motor  by  the  electric  current,  expressed 
in  watts,  is  equal  to  the  number  of  volts  P.D.  across  the  motor  multiplied  by  the  current  through  the 
motor  in  amperes. 

Express  the  input  also  in  horse  power,  remembering  that  746  watts  =  1  horse  power. 

Calculate  the  efficiency  of  the  motor ;  that  is,  the  ratio  of  the  output  to  the  input. 

Repeat  the  experiment,  using  a  considerably  higher  speed  and  a  smaller  pull  on  the  belt. 

[99] 


EXPERIMENT  37   (Continued} 

Questions,  a.   Is  the  efficiency  of  a  motor  the  same  for  different  speeds  ? 
6.  Would  its  efficiency  be  higher  if  there  were  no  atmosphere  ? 

c.  How  does  the  heat  generated  in  the  armature  and  field  windings  (H  =  .24  C2Rt)  affect  the  efficiency 
of  the  motor  ? 

d.  An  electric  automobile  is  run  for  five  hours.    During  this  time  the  motor  delivers  energy  at  an 
average  rate  of  2  H.P.    If  the  motor  has  an  efficiency  of  90%   and  the  storage  batteries  an  efficiency 
of  75°/0,  how  much  does  it  cost  to  charge  the  storage  batteries  sufficiently  for  this  trip,  if  the  cost  of 
the  electricity  used  in  charging  the  batteries  is  four  cents  per  kilowatt  hour. 


RECORD  OF  EXPERIMENT 


Output 

Circumference  of  belt  wheel  =  ...  ...ft. 


TRIAL 

READING  OF 
BALANCE  1 

READING  OF 
BALANCE  2 

PULL  ON  BELT 
IN  POUNDS 

FOOT  POUNDS 
PER  REVOLUTION 

R.P.M. 

FOOT  POUNDS 
PER  MINUTE 

HORSE  POWER 

Low  speed 

High  speed 

Input 


TRIAL 

P.D.  IN  VOLTS 

CURRENT  IN 
AMPERES 

WATTS 

HORSE  POWER 

Low  speed 

High  speed 

Efficiency  at  low  speed  = % 

Efficiency  at  high  speed  = % 


[lOOj 


EXPERIMENT  37  A 
A  STUDY  OF  A  SMALL  MOTOR  AND  DYNAMO 

I.  Adjustment  of  the  commutator.    Swing  the  permanent  field  magnets  away  from  the  armature  of 
the  motor  shown  in  Fig.  79.    Connect  one  dry  cell  to  the  motor.    With  a  small  compass  test  the 
polarity  of  each  end  of  the  armature  core  for  a  complete  revolution.   Note  the  position  of  the  arma- 
ture when  the  polarity  of  its  iron  core  changes. 

In  what  position  should  the  armature  core  be  when  its  polarity  changes  if  the  ends  are  to  be  acted 
upon  by  the  field  magnets  in  such  a  way  as  to  produce  continuous  rotation  ?  Turn  the  toppiece 
which  carries  the  brushes  until  the  point  of  commutation,  that  is,  the  position  where  the  insulating 
slits  of  the  commutator  pass  under  the  brushes,  is  at  the  proper  place. 

II.  Speed  of  rotation,    (a)  Now  swing  the  permanent  field  magnets  close  to  the  armature  and 
allow  the  motor  to  come  to  full  speed.  Then  gradually  swing  the  field  magnets  away  from  the  arma- 
ture and  explain  the  result. 

(5)  With  the  field  magnets  close  to  the  armature,  observe  the  effect  on  the  speed  of  the  motor 
of  reducing  the  current  through  the  armature.  This  may  be  accomplished  by  placing  a  resistance 


FIG.  79 


FIG.  80 


FIG.  81 


FIG.  82 


box,  or  rheostat,  of  from  4  to  40  cm.  of  No.  36  German-silver  wire  in  series  in  the  circuit.  Observe  the 
effect  on  the  speed  when  this  resistance  is  increased  from  1  ohm  to  10  ohms,  and  again  when  it  is 
decreased  from  10  ohms  to  1  ohm.  Explain. 

(c)  The  speed  may  also  be  changed  by  changing  the  point  of  commutation.  To  do  this  rotate  the 
top  which  carries  the  brushes.  How  does  this  affect  the  speed,  and  why  ? 

III.  Direction  of  rotation,    (a)  Reverse  the  current  through  the  armature.    Observe  and  explain 
the  effect  observed. 

(6)  Turn  each  field  magnet  end  for  end.  Explain  the  effect  which  doing  this  has  on  the  direction 
of  rotation. 

(<?)  What  effect  would  it  have  on  the  direction  of  rotation  if  the  current  through  both  the  arma- 
ture and  the  field  were  reversed  ?  If  in  doubt  try  the  experiment. 

IV.  Shunt-wound  motor,    (a)  Swing  the  permanent  field  magnets  out  of  the  way  and  connect  the 
electromagnet  in  parallel  with  the  armature  of  the  motor  as  in  Fig.  80.    Does  all  of  the  current  flow- 
ing from  the  battery  now  pass  through  the  armature  as  it  did  when  used  as  in  Fig.  79. 

(6)  Reverse  the  current  from  the  battery.  Observe  and  explain  the  effect,  if  any,  on  the  direction 
of  rotation. 

[101] 


EXPERIMENT  37  A    (Continued) 

V.  Seriec  wound  iflotor.    (V)  Connect  the  electromagnet  attachment  in  series  with  the  armature 
and  the  cells,  as  in  Fig.  81.    Does  all  of  the  current  now  flow  through  both  the  armature  and  the 
field  magnets  ? 

(6)  Reverse  the  current.    Explain  what  you  observe. 

VI.  Dynamo.    Remove  the  electromagnet  attachment,  swing  the  permanent  magnets  into  place, 
and  connect  the  motor  to  a  galvanometer,  as  in  Fig.  82.    Try  the  following  experiments. 

(<z)  Rotate  the  armature  in  one  direction  and  note  the  direction  of  deflection  of  the  galvanometer. 

(b*)  Rotate  the  armature  in  the  opposite  direction.    Observe  and  explain  the  effect. 

(<?)  Note  the  effect  on  the  deflection  of  the  galvanometer  of  swinging  the  permanent  magnets 
away  from  and  then  toward  the  rotating  armature.  Explain. 

(c?)  Is  the  deflection  the  same  for  all  speeds  of  rotation  ?   How  does  increasing  the  speed  affect  it  ? 

(e)  The  current  flowing  through  the  galvanometer  (and  consequently  the  deflection  in  each  of 
the  above  cases)  was  proportional  to  the  induced  E.M.F.  Name  as  many  factors  as  you  can  which 
affect  the  voltage  produced  by  a  dynamo. 


[1021 


EXPERIMENT  38 
SPEED  OF  SOUND  IN  AIR 

A.*  Let  the  class  be  divided  into  two  sections  and  placed  from  500  to  1000  m.  apart,  the  distance 
being  measured  by  laying  off  from  twenty-five  to  fifty  times  the  length  of  a  cord  20  m.  long.  Each 
group  should  be  provided  with  a  pistol,  blank  cartridges,  at  least  one  stop  watch,  and  a  thermometer. 
Let  a  member  of  one  group  raise  and  lower  a  handkerchief  three  times  as  a  ready  signal,  and  simul- 
taneously with  the  last  lowering  let  him  fire  a  pistol.  Let  a  member  of  the  other  group  take  with  a 
stop  watch  the  time  which  elapses  between  the  flash  and  the  report  of  the  pistol.  Then  let  the  opera- 
tions at  the  two  stations  be  interchanged,  in  order  to  eliminate  the  effect  of  any  wind  which  may 
be  blowing.  In  this  way  take  six  or  more  observations,  different  members  of  the  class  timing  the 
interval  in  turn.  Observations  which  differ  badly  from  the  general  average  and  which  are  evidently 
the  result  of  awkward  handling  of  the  stop  watch  need  not  be  included  in  the  final  mean.  From  this 
mean  compute  the  velocity  of  sound  at  the  temperature  of  the  air. 

B.  If  stop  watches  are  not  available,  set  up  a  heavy  pendulum  which  beats  seconds ;  attach  some 
white  object  to  it;  set  up  a  screen  so  that  the  pendulum  can  be  seen  only  when  it  is  passing  the 
middle  point  of  its  swing ;  let  one  student  stationed  near  the  pendulum  pound  loudly  on  some  sono- 
rous object  at  each  instant  at  which  the  pendulum  crosses  the  middle  point,  and  let  the  class  move 
away  until  the  beats  of  the  hammer  appear  again  to  coincide  with  the  passages  of  the  pendulum.  It  is 
obvious  that  the  distance  from  the  class  to  the  pendulum  is  numerically  equal  to  the  velocity  of  sound. 

Questions,  a.  Assuming  that  the  velocity  of  sound  increases  .6  m.  per  second  when  the  temperature  is 
increased  1°  C.,  compute  from  your  result  the  velocity  of  sound  at  0°  C. 

&.  What  would  be  the  difference  in  the  velocity  of  sound  on  a  hot  summer  day  when  the  thermometer 
registers  40°  C.  and  on  a  cold  winter  day  when  the  thermometer  registers  —  25°  C. 

*  Tarts  A  and  B  of  this  experiment  are  intended  as  alternatives,  the  choice  depending  upon  equipment. 


EXPERIMENT  39 


; 


FIG.  83 


VIBRATION  NUMBER  OF  A  TUNING  FORK* 

(«)  Smoke  the  glass  plate  A  (Fig.  83)  by  holding  it  in  the  flame  of  burning  gum  camphor  or  in 
gas  flame. t    Keep  the  plate  moving  back  and  forth  so  that  it  will  not  become  overheated  in  one 
lace  and  crack.    Lay  the  plate  on 

Je  board,  smoked  side  up,  and 
just  the  two  styluses  by  means 
of  the  clamps  B  and  C  until  they 
touch  the  plate  lightly,  very  near 
each  other  in  the  line  in  which  the  motion  is  to  take  place.  Set  the  tuning  fork  into  vibration  by 
striking  it  with  a  wooden  mallet,  or  by  bowing  with  a  violin  bow,  and  as  soon  thereafter  as  possible 
start  the  bob  to  vibrating,  and  draw  the  plate  beneath  the  bob  with  such  rapidity  that  the  trace  of 
three  or  four  complete  vibrations  of  the  bob  will  appear  on  the  plate. 

(5)  Count  the  number  of  vibrations  of  the  fork  corresponding  to  a  full  vibration  of  the  bob;  that 
is,  the  number  of  vibrations  of  the  fork  between  the  points  A  and  C  (Fig.  84),  then  between  B  and  Z>, 
then  between  C  and  E,  then  between 
D  and  F,  etc.,  estimating  in  every 
case  to  tenths  of  a  vibration.    Take 
a  mean  of  these  counts  as  the  num- 
:r  of  vibrations  of  the  fork  to  one 
the  bob. 

(c)  Repeat  the  observations  on  two  other  traces  and  take  the  mean  of  the  three  means  as  the 
>rrect  number  of  vibrations  of  the  fork  to  one  of  the  bob. 

(c?)  Get  the  rate  of  the  bob  by  counting,  with  the  aid  of  an  ordinary  watch,  the  number  of  vibra- 
tions which  it  makes  in  one  or  two  minutes,  or,  if  a  stop  watch  is  available,  by  taking  the  tune  of 
fifty  vibrations  of  the  bob. 

(e)  Compute  the  number  of  full  vibrations  made  by  the  fork  per  second. 


RECORD  OF  EXPERIMENT 

First  Trace  Second  Trace 


Third  Trace 


Number  of  Vibrations  of  Bob 


Vibrations  between  A  and  C  =  

Vibrations  between  B  and  D  =  

Vibrations  between  C  and  E  = 

Vibrations  between  D  and  F  = 

Means  =  

Final  mean  = 

Number  of  vibrations  of  bob  per  second  = 
.-.  rate  of  fork  = 


*  One  vibration-rate  apparatus  and  fifteen  glass  plates  will  suffice  for  a  class  of  thirty.  It  is  recommended  that  the 
instructor  make  the  traces  and  that  the  students  take  the  measurements. 

t  Instead  of  smoking  the  plate,  the  authors  often  mix  up  a  paste  of  whiting  or  chalk  dust  in  alcohol  and  paint  the  plate 
with  it.  This  brings  out  the  trace  quite  as  well,  and  the  whiting  is  very  much  cleaner  than  lampblack. 


[105] 


EXPERIMENT  40 
WAVE  LENGTH  OF  A  NOTE  OF  A  TUNING  FOEK 

(a)  Let  one  student  strike  a  C'  fork  (that  is,  one  which  makes  512  vibrations  per  second)  upon  a 
block  of  wood,  and  then  quickly  hold  it  above  the  tube  of  Fig.  85  with  the  flat  face  of  one  prong  just 

ve  the  end  of  the  tube.  (Use  the  tube  of  Fig.  9,  p.  7.)  Let  a  second  student 
ise  and  lower  the  vessel  A  while  the  fork  is  sounding,  and  note  as  accurately  as 
possible  the  shortest  length  of  the  air  column  which  gives  a  maximum  resonance. 
Mark  this  position  on  the  tube  by  means  of  a  small  rubber  band.  Test  the  correct- 
ness of  the  setting  by  several  observations. 

(5)  Locate  in  the  same  way  a  second  position  of  resonance  lower  in  the  tube, 
and  mark  with  a  rubber  band,  as  above.  Since  the  distance  between  two  positions 
of  maximum  resonance  is  exactly  one-half  wave  length,  twice  the  distance  between 
the  rubber  bands  will  be  equal  to  the  wave  length  of  the  note  sent  forth  by  the 
sounding  tuning  fork.  Compare  this  value  of  the  wave  length  with  that  computed 
by  dividing  the  speed  of  sound  at  the  temperature  of  the  room  by  the  vibration 
number  of  the  fork  as  marked  upon  it.  (Speed  of  sound  in  air  at  0°  C.  =  332  m. 
per  second.  It  increases  60  cm.  for  each  degree  of  rise  in  temperature.) 

(c)  Find  in  the  same  way  the  wave  length  of  a  fork  one  octave  lower  than  the  first. 


Fie.  85 


Questions,  a.    Explain  why  the  distance  between  the  rubber  bands  is  equal  to  one  half  of  the  wave 
length  of  the  sound  wave  sent  forth  by  the  sounding  tuning  fork. 

&.  Show  how  the  above  experiment  might  be  used  for  finding  the  velocity  of  sound. 

c.  Sound  travels  about  four  times  as  fast  in  hydrogen  as  in  air.    What  would  be  the  first  resonant 
length  for  the  C'  fork  used  above  if  the  tube  contained  hydrogen  ? 

d.  Since  the  speed  of  sound  is  the  same  for  notes  of  all  pitches,  what  conclusion  can  you  draw  from  your 
experiment  in  regard  to  the  vibration  frequencies  of  two  notes  which  are  an  octave  apart  ? 


RECORD  OF  EXPERIMENT 


First  Resonant 
Length  ^ 


Second  Resonant 
Length  lt 


Difference  x  2=  I 


Fork  No.  1  = 

Fork  No.  2  = 

Number  of  vibrations  of  fork  No.  1  = .-.  calculated  wave  length  = 

Number  of  vibrations  of  fork  No.  2  = .-.  calculated  wave  length  = 


[107] 


FIG. 


EXPERIMENT  41 
LAWS  OF  VIBRATING  STRINGS   • 

I.  Effect  of  length  on  the  vibration  rate  of  a  stretched  wire,    (a)  Stretch  a  fine  steel  piano  wire 
(No.  00)  along  the  board  A  (Fig.  86),  insert  a  bridge  at  5,  and  hang  a  pail  having  a  capacity  of  at 
least  six  quarts  over  the  pulley  p.    Pour  water  into  the  pail  until  the  note  given  by  the  wire  (best 
picked  near  the  middle)  is  in  unison  with  the  note  of  the  lowest  fork  provided ;  namely,  C.    Measure 
carefully   the    length    of    the   wire 

between  the  fixed  end  and  b.  i — 

ffl 

(6)  Move  the  bridge  b  until  the 
note  given  by  the  wire  is  exactly  in 
tune  with  a  fork  C',  an  octave  higher 
than  the  first  one.  Measure  and  record  the  length  from  the  fixed  end  of  the  wire  to  6. 

(c)  In  the  same  way  (that  is,  by  moving  6)  tune  the  wire  to  unison  with  a  third  fork  (for 
example,  G  above  middle  C)  and  measure  and  record  the  corresponding  length  of  the  wire. 

(d?)  From  a  study  of  the  measured  lengths  and  of  the  vibration  numbers  as  marked  on 
the  forks  find  and  state  in  your  notebook  the  law  connecting  the  rate  of  a  vibrating  string  with  its 
length  when  the  tension  is  kept  constant. 

II.  Effect  of  tension  on  the  vibration  rate  of  a  stretched  wire,    (a)  Set  up  side  by  side  two  boards 
like  A  (Fig.  86),  both  of  which  are  provided  with  No.  00  piano  wire.    Place  the  bridges  b  at  the  same 
distance,  say  60  cm.,  from  the  left  end  of  each.   Produce  the  same  tension  in  the  two  wires  by  hanging 
from  each  a  like  weight  (for  example,  a  pail  containing  a  small  amount  of  water).    The  weights  should 
be  of  such  size  as  to  produce  in  the  plucked  wires  a  low  but  perfectly  distinct  musical  note.    Bring 
the  two  wires  into  exact  unison  by  adjusting  the  water  in  one  of  the  pails  until  no  beats  are  heard 
when  the  strings  are  sounded  together.    Find  the  exact  tension  on  one  of  the  wires  by  weighing  the 
pail  and  water  carefully  with  a  spring  balance.   Produce  the  exact  octave  on  the  other  wire  by  moving 
the  bridge  until  the  wire  is  only  one  half  as  long  as  at  first.    Bring  the  first  wire  into  unison  with  it 
by  adding  water  to  the  pail,  leaving  the  length  exactly  as  at  first.    Weigh  the  pail  and  water  again, 
and  find  the  ratio  of  the  weights  in  the  two  cases.    In  order  to  double  the  rate,  how  many  times  has 
it  been  necessary  to  multiply  the  stretching  force  ? 

(5)  Make  the  second  wire  just  two  thirds  its  original  length,  its  tension  still  being  kept  constant. 
In  what  ratio  will  this  change  its  vibration  number  ?  Adjust  the  amount  of  water  in  the  pail  hanging 
from  the  first  wire  until  the  two  are  in  unison,  and  weigh  on  the  spring  balance  again. 

From  the  law  suggested  in  (a)  calculate  what  this  last  stretching  weight  should  have  been  and  see 
how  well  it  agrees  with  the  observed  value. 

Questions,    a.  For  the  high  notes  on  a  piano  does  the  manufacturer  use  long  or  short  wires  ?    Why  ? 
b.  State  in  your  notebook  the  laws  deduced  from  I  and  IL 


I.  Effect  of  length 

Length  of  C  wire  =  

Length  of  C'  wire  = 

Length  of  G  wire  =  

Calculated  length  of  C'  wire  = cm. 

Calculated  length  of  G  wire  = cm. 


RECORD  OF  EXPERIMENT 

II.  Effect  of  tension 


.  cm. 
.cm. 
.cm. 


First  stretching  weight  = g. 

Second  stretching  weight  = g. 

Second  divided  by  first  =  g. 

Third  stretching  weight  (calculated)  = g. 

Third  stretching  weight  (observed)    = go 


[109] 


EXPERIMENT  42 
LAWS  OF  REFLECTION  FROM  PLANE  MIRRORS 

I.  To  prove  that  the  angle  of  incidence  equals  the  angle  of  reflection,    (a)  Blacken  one  side  of  a  strip 
of  plate  glass  or  a  microscope  slide ;  attach  it  by  means^of  a  rubber  band  to  a  small  wooden  block,  and 
then  set  it  on  edge  so  that  the  line  A  C  (Fig.  87),  drawn  on  a  sheet  of  paper,  coincides  with  the  plane 
of  the  unblackened  face.    The  rear  face  is  blackened  in  order  to  prevent  reflection  from  that  face  and 
enable  one  to  work  with  the  light  reflected  from  the  front  face  alone. 

Set  a  pin  at  a  point  B  against  the  face  of  the  glass.  Set  another  pin  at 
any  point  P,  and  then,  placing  the  eye  so  as  to  sight  along  B  and 
P",  the  image  of  P,  set  a  third  pin  P'  somewhere  in  this  line  of  sight. 
Remove  the  glass  plate,  and  with  a  protractor  or  a  pair  of  dividers 
construct  a  perpendicular  BE  to  AC  at  the  point  B.  Draw  PB  and 
P'B  and  measure  the  angle  of  incidence  PBE  and  the  angle  of  reflec- 
tion P'BE  with  the  protractor.  If  a  protractor  is  not  at  hand,  draw  an 
arc  with  B  as  a  center,  cutting  the  lines  PB  and  P'B  at  M  and  0, 
and  measure  the  lines  MN  and  ON. 

(6)  Repeat  for  some  other  position  of  P. 

(c)  Finally,  set  P  at  such  a  point  that  it  is  directly  in  line  with  its  own  image  P"  and  B.  Draw 
the  line  PB  and  also  construct  the  perpendicular  to  A  C  at  B.  If  the  angle  of  incidence  is  equal  to 
the  angle  of  reflection,  the  two  lines  should  exactly  coincide. 

II.  To   locate  the   image  formed   by  a   plane   mirror, 
(a)  Again  set  up  the  pin  at  P  (Fig.  88),  draw  the  line 
AC,  and  place  the  edge  of  the  mirror  upon  it;  then  lay  a 
straightedge  on  the  paper  in  successive  positions  ab,  cd,  ef, 
etc.,  such  that  the  image  P"  always  appears  to  lie  in  the 
prolongation  of  the  edge  of  the  ruler.   Draw  the  correspond- 
ing lines  ab,  cd,  etc. ;  then  remove  the  glass  and  locate 
the  image  P"  by  prolonging  these  lines  to  their  point  of 
intersection. 

(5)  Measure  the  perpendicular  distance  from  P  to  AC  and  from  P"  to  AC.  Also  measure  the 
angle  which  PP"  makes  with  AC. 

Tabulate  your  results  neatly,  and  state  the  conclusions  which  you  draw  from  I  and  II. 


P" 


[111] 


EXPERIMENT  43 

TO  FIND  THE  RATIO  OF  THE  VELOCITIES  OF  LIGHT  IN  AIR  AND  GLASS  (INDEX  OF 

REFRACTION  OF  GLASS) 

Draw  a  straight  line  AC  (Fig.  89)  across  a  large  sheet  of  paper  and  set  one  edge  of  the  plate- 
glass  prism  mnO  in  exact  coincidence  with  it.  Lay  a  ruler  on  the  paper  in  such  a  position  that,  as 
you/sight  along  its  edge  from  some  position  E  in  the  plane  mnO,  the  apex  0  of  the  prism,  as  seen  in 
the  face  mn,  appears  to  lie  in  the  prolongation  of  the  edge  of  the  ruler.  Draw  a  fine  line  ab  along  this 
edge.  Then  move  the  eye  to  a  position  E\  about  as  far  to  the  right 
as  E  was  to  the  left  of  the  normal  to  mn,  and  draw  in  the  same  way 
a  line  cd.  Mark  the  position  of  0  carefully  by  means  of  a  pin  prick. 
Then  remove  the  prism,  and  with  an  accurate  straightedge  and  a  very 
sharp  pencil  or  knife-edge  prolong  ab  and  cd  until  they  meet  in  some 
point  0'.  The  point  0  is  then  the  center  in  the  glass  of  the  light  waves 
by  means  of  which  you  see  the  apex  0,  while  the  point  0'  is  the  center 
of  the  same  waves  after  they  have  emerged  into  air.  If,  therefore,  from 
0  and  0'  as  centers,  the  two  arcs  qrt  and  qr't  are  constructed,  the  arc 
qrt  would  represent  the  shape  and  position  of  the  wave  from  0  when 
it  has  reached  the  points  q  and  t,  if  the  speed  in  air  were  the  same  as 
the  speed  in  glass,  while  qr't  is  the  actual  position  .of  this  wave  in 
view  of  the  fact  that  light  travels  faster  in  air  than  in  glass,  sr'/sr 
is  then  the  ratio  of  these  two  speeds.  But  sr'/sr  is  also  the  ratio  of 
the  curvatures  of  the  arcs  qr't  and  qrt ;  that  is,  it  is  the  ratio  of  the 
amounts  by  which  these  curved  lines  depart  from  the  straight  line  qst. 

Now  if,  at  a  given  point,  one  arc  is  curving  twice  as  rapidly  as  another,  it  is  evident  that  its  center 
can  be  but  half  as  far  away ;  that  is,  the  curvatures  of  two  arcs  are  always  inversely  proportional  to 
their  radii.  Hence  the  ratio  sr'/sr  is  the  same  as  the  ratio  Oq/0'q.  Measure  these  distances  as  care- 
fully as  possible  with  a  meter  stick,  and  record  your  value  for  the  ratio  of  the  velocities  of  light  in  air 
and  glass.  This  is  called  the  index  of  refraction  of  glass.  Repeat  the  observations,  using  different 
positions  of  E  and  E\  and  see  how  well  the  two  observations  agree. 


RECORD  OF  EXPERIMENT 

First  Trial                                 Second  Trial 
Oq        = Oq        =  

O'q       =  O'q       ~  

Index  =  ...  Index  =  ...  Mean  value  of  index 


Per  cent  of  difference  between  first  and  second  = 


[1131 


EXPERIMENT  44 
THE  CRITICAL  ANGLE   OF  GLASS 

Place  the  plate-glass  prism  ABC  (Fig.  90),  having  three  polished  faces,  upon  a  large  sheet  of 
paper  in  front  of  a  window  OR  through  which  the  sky  is  visible.  If  desired,  OR  may  be  a  piece  of 
ound  glass  behind  which  a  white  light  is  placed.  Place  the  eye  in  a  position  E,  so  as  to  observe  the 
age  of  the  sky  or  ground  glass  as  it  is  seen  by  reflection  from  AB.  A  bluish-green  line  will  be  seen 
dividing  AB  into  two  parts  of  markedly 
different  brightness. 

The  part  to  the  right  is  brighter  than 
the  part  to  the  left.  If  this  line  dividing 
the  field  is  not  seen  at  first,  it  will  appear 
on  moving  the  eye  to  the  left  or  the  right. 
Move  the  eye  about  until  the  green  edge 
of  this  line  is  brought  into  exact  coincidence 
with  a  small  ink  spot  placed  at  s  on  the 
face  AB.  From  the  figure  it  will  appear 
that  the  light  which  comes  to  the  eye  by 
reflection  from  the  various  points  along  AB 
must  make  a  larger  and  larger  angle  of 
incidence  on  AB  as  the  point  considered 
lies  farther  and  farther  to  the  right  of  A. 

When  this  angle  is  equal  to  or  greater  than  the  critical  angle,  as  is  the  case  between  s  and  B,  the 
whole  of  the  light  incident  upon  AB  is  reflected ;  when  it  is  less  than  the  critical  angle,  as  is  the  case 
between  A  and  s,  part  is  reflected  and  part  transmitted.  The  bluish-green  line  which  separates  the  field 
into  parts  of  unequal  brightness  represents  the  position  on  AB  at  which  total  reflection  begins ;  that  is, 
the  angle  i  is  the  critical  angle  for  glass.  To  measure  this  angle,  lay  a  ruler  so  that  its  edge  appears 
to  lie  in  the  same  straight  line  with  the  point  *  and  the  green  edge  of  the  line  in  the  field,  and  mark 
with  a  line  on  the  paper  the  position  En  of  the  straightedge.  Then  with  a  sharp  pencil  or  a  knife 
draw  an  outline  ABC  of  the  prism  upon  the  paper,  and  place  a  pin  prick  at  8  just  beneath  the  ink 
spot  s  on  the  face  AB.  Remove  the  prism  and  extend  En,  the  line  just  drawn,  until  it  meets  AC  at 
some  point  n.  Connect  this  point  n  with  the  pin  prick  at  s,  erect  the  perpendicular  upon  AB  at  s,  and 
measure  with  the  protractor  the  angle  i.  This  is  the  critical  angle  for  glass. 

Extend  the  lines  m  and  the  perpendicular  at  s  so  as  to  make  them  from  6  in.  to  1  ft.  in  length. 
Draw  uv  parallel  to  AB.  Then  us/uv  should  give  the  same  value  for  the  index  of  refraction  as  that 
obtained  in  the  last  experiment.  The  proof  of  this  statement  is  not  suitable  for  an  elementary  text, 
but  the  measurement  will  furnish  an  interesting  check  as  to  the  accuracy  of  the  results  of  the 
experiment. 


[-116] 


EXPERIMENT  45 
FOCAL  LENGTH  OF  A  CONCAVE  MIRROR 

I.  Support  the  concave  mirror  in  direct  sunlight  by  means  of  a  clamp  and  let  the  image  of  the 
sun  be  thrown  upon  a  narrow  strip  of  paper  held  in  front  of  the  mirror.    Measure  the  distance  from  the 
mirror  to  the  point  at  which  the  spot  of  light  on  the  thin  strip  is  smallest  and  brightest.   This  distance 
is  the  focal  length;  designate  it  by  the  letter/. 

II.  Throw  the  image  of  a  distant  house  on  the  thin  strip  of  paper  in  the  same  way.    Repeat  the 
above  measurement. 

III.  Place  a  candle  flame  or  an  electric  light  at  a  distance  J>0,  about  three  times  the  focal  length 
from  the  mirror,  and  locate  the  position  of  the  image  by  letting  it  fall  on  the  narrow  screen.   Compute 
the  focal  length  from  the  formula  ^         ..        .. 

^+D=f' 

in  which  D0  and  D{  are  the  distances  of  the  object  and  image  respectively  from  the  center  of  the  mirror. 

IV.  Set  up  a  pin  on  a  block  so  that  its  head  is  nearly  opposite  the  middle  of  the  mirror.   Move  the 
pin  out  to  about  twice  the  focal  length  of  the  mirror.    If  the  eye  is  placed  in  front  of  the  mirror  and 
as  much  as  8  or  10  in.  farther  from  it  than  the  pin,  the  object  and  image  may  both  be  seen  —  the 
image  inverted  and  the  object  erect,  in  the  manner  shown  in  another  connection  in  Fig.  92.    Shift  the 
position  of  the  pin  or  of  the  mirror  until  the  image  of  the  head  of  the  pin  is  exactly  in  line  with 
the  head  of  the  pin  itself.    Move  the  eye  to  the  right  and  left  and  see  whether  there  is  any  relative 
motion  of  the  pin  and  its  image.    If  so,  it  is  because  they  are  not  the  same  distance  from  the  eye. 
The  one  which  is  farther  away  will  move  to  the  left  when  the  eye  is  moved  to  the  left,  and  to  the 
right  when  the  eye  is  moved  to  the  right,    (Test  the  correctness  of  the  above  statement  by  holding 
two  pencils  in  line,  but  at  different  distances  from  the  eye,  and  noticing  how  they  appear  to  move 
with  reference  to  each  other  as  the  eye  is  moved  from  side  to  side.)    Adjust  the  position  of  the  pin 
until  there  is  no  relative  motion  between  the  pin  and  its  image  as  the  eye  is  moved  from  side  to  side. 
The  image  of  the  pin  is  now  at  the  same  place  as  the  pin  itself ;  hence  the  pin  must  be  at  the  centei 
of  curvature  of  the  mirror.    Measure  the  distance  from  pin  to  mirror.    This  distance  is  the  radius  of 
curvature  of  the  mirror.    Find  what  relation  exists  between  this  distance  and  the  focal  length  of  the 
mirror. 

RECORD  OF  EXPERIMENT 

Focal  length,  by  I    = Focal  length,  by  III 

Focal  length,  by  II  = One  half  of  radius  of  mirror  =  


117] 


EXPERIMENT  46 
LAWS  OF  IMAGE  FORMATION  IN  CONVEX  LENSES 

I.  Set  up  in  the  positions  shown  in  Fig.  91  a  wire  netting  0,  a  reading  glass  L  of  about  15  cm. 
focus,  and  a  block  B  provided  with  a  paper  scale  s.     Set  a  gas  flame  behind  0  to  insure  bright 


illumination.  Adjust  B  and  L  until 
measure  D0,  the  distance  from  0  to 
to  s.  Next  read  on  s  the  number  of 
image  of  the  netting.  Then  with 
by  the  same  number  of  squares  on 


the  image  of  the  netting  is  sharply  outlined  on  «.  Then 
the  middle  of  the  lens  L,  and  J>t.,  the  distance  from  L 
millimeters  covered  by  ten  or  twenty  squares  in  the 
another  scale  measure  the  number  of  millimeters  covered 
the  netting  0.  These  two  observations  give  respectively 


FIG.  91 


FIG.  92 


the  length  L{  of  the  image  and  the  length  L0  of  the  object.  Repeat  the  same  observations  with  three  or 
four  different  values  of  D0,  such  as  30  cm.,  40  cm.,  50  cm.,  and  60  cm.,  and  calculate  the  focal  length 
/  of  the  lens  from  the  formula 

1+1.1. 

j>.  -»,  / 

Also  take  the  ratios  L0/L{  and  D0/D{  and  tabulate  as  indicated  in  the  Record  of  Experiment. 
What  conclusion  do  you  draw  from  the  last  two  columns  ? 

II.  Find  the  focal  length  of  the  lens  directly  by  removing  0  and  casting  the  image  of  a  distant 
chimney  or  house  upon  s. 

III.  As  a  final  check  on  the  focal  length,  place  a  plane  mirror  behind  the  lens  and  mount  a  pin 
in  front  of  the  lens  opposite  its  center.    Adjust  the  pin  by  the  method  of  parallax  (the  method  used 
in  Exp.  45,  IV),  until  the  image  of  the  head  of  the  pin  coincides  with  the  head  of  the  pin  itself.    The 
distance  from  the  pin  to  the  center  of  the  lens  must  then  be  equal  to  the  focal  length  of  the  lens,  as 
is  shown  by  the  diagram  (Fig.  92),  since  the  waves  between  the  lens  and  the  mirror  are  plane. 


RECORD  OF  EXPERIMENT 


-Do 

-Di 

J),  +  Di 

/ 

Lo 

Li 

Lo 
Tt 

D, 
Di 

Focal  length  (mean  of  co 

lumn  4)  —                .           cm.,  by  II  —  cm.,  by  III  =  cm. 

[119] 

EXPERIMENT  47 
MAGNIFYING  POWER  OF  A  SINGLE  CONVEX  LENS 

Fig.  93  shows  a  so-called  linen  tester  —  a  single  convex  lens  at  the  focus  of  which  is  a  square 
hole  in  a  brass  frame.  Support  the  linen  tester  with  a  tripod  and  a  clamp  so  that  the  lens  of  the  linen 
tester  is  25  cm.  from  the  table  top.  Place  a  meter  stick  on  the 
table  directly  below  the  linen  tester  (Fig.  93). 

Place  the  eye  as  close  as  possible  to  the  lens  and  with  both 
eyes  open  observe  how  many  millimeters  on  the  stick  seen  with  one 
eye  are  covered  by  the  hole  seen  through  the  lens  with  the 
other  eye. 

Divide  the  number  thus  seen  by  the  measured  width  of  the 
hole  in  millimeters.  This  is  obviously  the  magnifying  power, 
expressed  in  diameters,  of  the  lens,  since  it  shows  how  many  times 
as  large  a  diameter  of  the  object  appears  when  seen  through  the 
lens  as  when  viewed  with  the  naked  eye  at  the  distance  of  most  FlG  93 

distinct  vision ;  namely,  25  cm.    Measure  as  accurately  as  possible 

the  focal  length  /  of  the  lens  (that  is,  the  distance  from  the  middle  of  the  lens  to  the  hole)  and  see 
how  well  the  observed  magnifying  power  agrees  with  the  theoretical  value ;  namely,  25//?. 


EECORD  OF  EXPERIMENT 

Number  of  millimeters  covered  by  the  hole  on  the  meter  stick  = 

Width  of  the  hole  in  millimeters  = 

.-.  magnifying  power  in  diameters  (experimental  value)  = 

Focal  length  of  lens  in  centimeters  =  

.-.  magnifying  power  in  diameters  (theoretical  value)  =  , 


[121] 


FIG.  94 


EXPERIMENT  48 
THE  ASTEONOMICAL  TELESCOPE  ' 

I.  To  construct  a  telescope.    With  the  simple  magnifying  glass  used  in  the  last  experiment  and 
ith  an  objective  consisting  of  the  reading  glass  of  Exp.  46,  construct  an  astronomical  telescope,  as 
Hows :  Set  the  reading  glass  in  some  support  (Fig.  94)  and  find,  with  the  aid  of  a  piece  of  white 

board,  the  distance  F  from  the  lens  at  which  the  image 
a  distant  building  or  window  is  formed.  Then  set  up 
the  linen  tester  behind  the  card  at  its  focal  length  /  from  it. 
Now  remove  the  card  and  view  the  image  of  the  distant 
object  through  the  eyepiece.  Slide  the  eyepiece  support, 
if  necessary,  until  the  distant  object,  preferably  a  brick 
wall,  is  very  sharply  seen;  then  measure  the  distance 
between  the  lenses  and  compare  this  distance  with  the 
sum  of  the  focal  lengths.  Do  you  find  any  simple  relation 
between  these  quantities  ?  Can  you  see  any  reason  why 
there  should  be  some  such  relation  ?  Explain. 

II.  To  measure  the  magnifying  power  of  the  telescope. 

Focus  the  telescope  upon  two  heavy  horizontal  marks  drawn,  for  example,  on  a  blackboard  on  the 
opposite  side  of  the  room.  Let  the  lines  be  from  3  to  6  in.  apart.  When  the  lenses  have  been 
adjusted  so  that  a  distinct  image  of  the  marks  is  seen  with  the  eye  which  is  looking  through  the 
telescope,  open  the  other  eye  and  direct  another  student  to  make  on  the  board  marks  which  shall 
coincide  with  the  apparent  positions  on  the  board  of  the  images  of  the  two  marks  as  seen  through  the 
telescope.  It  may  be  found  difficult  at  first  to  give  attention  to  both  eyes  at  once,  but  a  little  practice 
will  make  it  easy.  Repeat  several  times  and  compute  the  magnifying  power  M  from  each  observation. 
Compare  this  magnifying  power  with  the  theoretical  value  for  the  magnifying  power  of  a  telescope  ; 
that  is,  the  ratio  of  the  focal  lengths  of  the  objective  and  the  eyepiece.  Determine  these  focal  lengths 
by  casting  the  image  of  a  distant  object  on  a  small  screen  or  a  sheet  of  paper. 


RECORD  OF  EXPERIMENT 
I.  Distance  between  lenses      = cm.;  F  +  f= 

II.  M  (observed)  =  diameters. 

F 
M  (theoretical),  that  is,  — ,  = diameters. 


.cm. 


[123] 


EXPERIMENT  49 


I.  To  construct  a  microscope.    Place  two  corks  which  contain  holes  about  1  cm.  in  diameter  in  the 
ends  of  a  cardboard  or  tin  tube  4  or  5  in.  long,  and  with  the  aid  of  a  rubber  band  fix  the  lenses  of 
two  of  the  linen  testers  over  the  holes  (Fig.  95).    Support  the  tube  vertically  over  the  table  by  means 
of  clamps,  and  raise  or  lower  it  until  a  magnified  image  of  a  millimeter 

scale  lying  on  a  block  beneath  it  is  in  sharp  focus,  the  distance  from  the 
table  to  the  top  of  the  tube  being  somewhat  more  than  25  cm. 

II.  To  determine  its  magnifying  power,    (a)  Lay  a  meter  stick  on  the 
table,  as  in  Fig.  95,  and  elevate  one  end  of  it  until  the  distance  to  the 
stick  from  the  eye  which  is  not  looking  through  the  microscope  is  exactly 
25  cm.    By  fixing  the  attention  simultaneously  on  the  two  scales  seen, 
one  through  the  microscope  and  the  other  with  the  unaided  eye,  determine 
how  many  millimeters  on  the  meter  stick  *  are  covered  by  1  mm.  of  the 
scale  seen  in  the  microscope ;  that  is,  find  the  number  of  diameters  of 
magnification  of  the  microscope. 

(5)  If  ^  is  the  distance  from  the  objective  to  the  focal  plane  of  the 
eyepiece,  that  is,  the  distance  between  the  centers  of  the  lenses  minus  the 
focal  length  f  of  the  eyepiece,  and  if  12  represents  the  distance  from 

the  objective  to  the  object  viewed,  then  ljlz  represents  how  many  times  the  image  formed  by  the 
objective  is  larger  than  the  object.    Since  the  eyepiece  magnifies  this  image  25//  times,  the  total 
magnifying  power  M  of  the  compound  microscope  should  be  25/f  X  ljl$    Measure  lr  and  Z2  and  com 
pare  the  observed  value  of  M  with  this  calculated  value. 


FIG.  95 


RECORD   OF  EXPERIMENT 

(a)  Observed  magnifying  power  by  comparing  scales  =  ........................  diameters. 


cm.; 


cm.; 


25  I 


f  =  ........................  cm.  ;  .•.  M  =  -  *•  =  ........................  diameters. 

*  The  distance  on  the  meter  stick  which  is  covered  by  1  mm.  of  the  scale  when  viewed  through  the  microscope  may  also 
be  found  by  marking  the  projection  of  the  two  millimeter  marks,  as  seen  through  the  microscope,  on  a  sheet  of  paper  set 
26  cm.  from  the  eye,  and  then  measuring  the  distance  in  millimeters  between  these  two  marks  on  the  paper.  The  magnifying 
power  M  expressed  in  diameters  is  then  obviously  equal  to  the  above-measured  distance  expressed  in  millimeters. 


r  .125 1 


EXPERIMENT  50 


FIG.  96 


PRISMS 

I.  Path  of  a  beam  of  light  through  a  prism.    Draw  a  line  AC  (Fig.  96)  on  a  page  of  your 
notebook.    Place  the  prism  on  the  paper  in  the  position  indicated  in  the  figure.    Light  coming  to  the 
prism  in  the  direction  AC  will  be  bent  both  upon  entering  and  upon  leaving  the  prism.   Place  a  ruler 
on  the  paper  and  adjust  it  carefully  until  it  is  exactly  in  line  with  the 

apparent  direction  of  A  C  as  seen  through  the  prism.  With  a  sharp 
pencil  draw  a  line  DE  along  the  edge  of  the  ruler,  and  trace  the  outline 
of  the  prism  on  the  paper.  Remove  the  prism  and  extend  the  lines  AC 
and  DE  until  they  meet  at  /  and  #,  the  lines  which  represent  the 
prism  faces.  Then  AfgE  will  be  the  path  of  the  light  which  traverses 
the  prism. 

II.  Dispersion,    (a)  With  the  aid  of  the  knowledge  gained  in  I,  place  the  prism  in  direct  sunlight 
in  such  a  way  that  the  beam  from  the  sun  is  thrown  upon  some  shaded  portion  of  the  floor.    Place 
between  the  prism  and  the  sun  a  sheet  of  cardboard  containing  a  horizontal  slit  2  or  3  mm.  wide. 
Name  the  colors  which  you  see  upon  the  floor  and  into  which  the  sunlight  has  been  resolved. 
Which  has  suffered  the  largest  bending  in  passing  through  the  prism,  and  which  the  smallest? 
Cut  two  2-mm.  slits  in  the  cardboard  and  leave  a  2-mm.  space 

between  them.  Cover  one  slit  and  note  the  spectrum;  then 
uncover  the  slit  and  note  the  change  in  color  in  the  middle  of  the 
patch  where  the  two  spectra  overlap.  Does  this  show  that  the  spec- 
tral colors  may  be  recombined  into  white  light  ?  Hold  the  prism 
alone,  without  any  slit,  in  the  sunlight.  Explain  now  why  only 
the  edges  of  the  patch  appear  colored,  while  the  middle  appears 
uncolored. 

(5)  Now  place  the  prism  immediately  before  the  eye  in  such 

a  way  that  you  can  observe  through  it  a  narrow  (2-mm.)  strip  of  white  paper  placed  on  a  black  back- 
ground, or,  better  still,  an  electric-lamp  filament  or  the  narrow  edge  of  a  gas  flame.  Explain  why  the 
red  now  appears  to  be  on  the  side  next  the  base  of  the  prism,  while  the  blue  is  nearer  the  apex. 
Substitute  a  broad  sheet  of  paper  for  the  narrow  strip.  When  viewed  through  the  prism,  one  edge  will 
appear  red,  shading  into  yellow  on  the  inner  side,  and  the  other  will  appear  blue,  shading  into  green. 
Explain  why  the  paper  does  not  appear  colored  in  the  middle,  while  it  does  appear  colored  at  the 
edges.  Explain  further  why  the  two  edges  are  differently  colored. 

III.  Bright-line  spectra'.    Let  one  student  hold  successively  in 
a  Bunsen  flame,  arranged  as  in  Fig.  97,  three  platinum  wires  or  bits 
of  asbestos,  which  have  been  dipped,  one  in  a  solution  of  common 
salt  (sodium  chloride),  another  in  lithium  chloride,  and  another  in 
calcium  chloride,  taking  care  that  the  wire  itself  is  kept  below  the 
lower  edge  of  the  slit  s.   Let  other  students  look  through  the  prisms 
at  distances  of  about  10  ft.,  in  the  manner  indicated  in  the  figure, 

and  record  the  character  of  the  spectra  to  which  the  incandescent  vapors  of  these  substances  give  rise. 

IV.  Path  of  a  beam  of  light  through  a  plate  of  glass  with  parallel  faces,    (a)  Place  two  prisms 
together  in  the  manner  shown  in  Fig.  98,  thus  forming  in  effect  a  single  piece  of  glass  with  the  parallel 
edges  om  and  pn.   Draw  a  heavy  line  AB,  then  place  a  straightedge  in  line  with  the  image  of  this  line, 
and  draw  a  mark  A'B'  along  its  edge,  showing  the  direction  of  the  light  after  passing  through  the 

[127] 


FIG.  97 


FIG.  98 


EXPERIMENT  50    (Continued) 

parallel  faces  om  and  pn.    From  the  result  obtained,  state  what  happens  to  the  direction  of  a  ray  of 
light  which  passes  through  a  plate  of  glass  with  parallel  faces. 

(5)  Slide  the  two  prisms  along  om  until  the  line  AB  meets  the  first  prism  nearer  its  apex.  Then 
slide  the  other  prism  along  the  common  face  until  the  perpendicular  distance  between  the  faces  mo 
and  pn  is  just  one  half  as  much  as  before, 
as  shown  in  Fig.  99.  With  the  same 
line  AB  and  the  face  om  exactly  parallel 
to  its  initial  position,  draw  again  a  line 
A'B'  in  the  apparent  prolongation  of  AB. 

(c)  Slide  the  prisms  into  the  position 
shown  hi  Fig.  100,  being  very  careful  to 
keep  the  face  om  parallel  to  its  initial 
direction.  The  thickness  of  glass  to  be 
traversed  will  now  be  three  times  as  great  as  in  (T).  Proceed  precisely  as  in  (a)  and  (£)  above. 

(c?)  Remove  the  prisms  and  prolong  AB.  Measure  the  perpendicular  distances  between  AB  arid 
the  three  prolongations  of  AB  as  seen  through  the  three  thicknesses  of  glass.  State  in  what  way  the 
experiment  shows  that  the  lateral  displacement  of  the  beam  varies  with  the 
thickness  of  the  glass. 

(e)  If  the  prisms  are  so  placed  that  AB  is  perpendicular  to  the  face  om 
(Fig.  101),  no  trace  of  the  line  can  be  seen  at  A'B'.  But  if  a  drop  of  water  is 
placed  between  the  faces  in  contact  along  mp,  the  line  AB  can  be  seen  very 
plainly  at  A'B'.  Explain,  remembering  that  the  critical  angle  for  rays  of  light 
passing  from  glass  to  air  is  about  42°,  while  it  is  about  62°  for  rays  passing  from  glass  to  water. 

If,  now,  A'B'  is  drawn  as  above  and  if  AB  is  exactly  perpendicular  to  om,  then  on  removing  the 
prisms  and  extending  AB  it  will  be  found  that  AB  and  A'B'  lie  on  the  same  straight  line ;  that  iss 
there  has  been  no  lateral  displacement.  Why  ? 


FIG. 


FIG.  100 


[128] 


EXPERIMENT  51 


TO  MEASURE  THE  CANDLE  POWER  OF  A  WELSBACH  BURNER  AND  OF  AN  ORDINARY 
OPEN  GAS  FLAME  AND  TO  COMPARE  THEIR  COST  OF  OPERATION  WITH  THAT  OF  A 

TUNGSTEN  LAMP 

I.  The  Welsbach  burner.  Place  a  40  watt  (34  C.P.),  or  a  60  watt  (53  C.P.),  tungsten  lamp  * 
at  A,  and  a  Welsbach  burner  at  B  (see  Fig.  102).  The  Welsbach  burner  should  be  connected  to 
the  gas  meter  used  in  Exp.  18. 


FIG.  102 

Slide  the  photometer  C  along  the  optical  bench  until  the  spot  or  cross  in  the  photometer  appears 
as  nearly  as  possible  the  same  on  both  sides.  When  in  this  position  the  spot  is  evidently  illuminated 
equally  by  each  light.  Measure  and  record  the  distances  AC  and  BC.  If  the  optical  bench  has  a 
graduated  bar,  these  distances  may  be  read  directly  on  the  bar. 

With  a  watch  observe  the  length  of  time  required  for  1  cu.  ft.  of  gas  to  pass  through  the  burner, 
using  the  tungsten  lamp  for  the  source  of  known  candle  power. 

Compute  the  candle  power  of  the  Welsbach  burner  by  use  of  the  equation 

C.P.  of  source  of  light  at  A  _  AC 
C.P.  of  source  of  light  at  B      B(jz 

II.  The  ordinary  open  gas  flame.  Replace  the  Welsbach  burner  by  an  ordinary  open  gas  flame 
and  make  a  set  of  observations  and  calculations  similar  to  those  made  in  I. 

Questions,  a.  From  your  data  calculate  the  number  of  cubic  feet  of  gas  consumed  per  hour  by  the 
Welsbach  burner  and  also  by  the  open  gas  flame. 

6.  At  the  price  charged  by  your  local  gas  company  for  gas  compute  the  cost  of  operating  for  500  hr. 
a  Welsbach  burner  like  that  used  above.  What  is  the  cost  per  candle  power  for  the  same  length  of  time  ? 

c.  What  is  the  cost  per  candle  power  of  operating  the  open  gas  flame  for  500  hr.  ? 

d.  At  the  price  charged  by  your  local  power  plant  for  electricity  what  is  the  cost  per  ca'ndle  power  of 
operating  for  500  hr.  the  tungsten  lamp  used  above  ? 

e.  Which  of  the  three  sources  of  light  referred  to  in  Questions  b,  c,  and  d  has  the  lowest  cost  of  opera- 
tion per  candle  power  ? 

/.  After  taking  into  account  the  cost  of  the  mantles  required  to  operate  a  Welsbach  lamp  for  500  hr. 
and  also  the  cost  of  the  tungsten  lamps  which  will  give  about  the  same  candle  power,  which  method  of  light- 
ing is  the  cheaper  ?  This  method  is  approximately  how  many  per  cent  cheaper  than  the  other  method  ? 

*  Accurately  standardized  electric  lamps  are  unnecessary  for  this  experiment,  since  the  relative  candle  powers  of  the  two 
sources  at  A  and  B  does  not  depend  upon  knowing  the  exact  candle  power  of  the  tungsten  lamp.  Therefore  the  relative  cost 
per  candle  power  of  operating  different  lamps  is  obtained  accurately  by  using  the  ordinary  commercial  lamp  as  a  standard 
and  using  for  its  candle  power  the  value  given  by  the  maker. 

[129] 


EXPERIMENT  51    (Continued) 

RECORD  OF  EXPERIMENT 
I.  The  Welsbach  burner 

Candle  power  of  tungsten  lamp  = ,  AC  = ,  EC  = 

.•.  candle  power  of  Welsbach  lamp  =  

Time  required  to  consume  ^  cu.  ft.  of  gas  = 

II.  The  open  gas  flame 

Candle  power  of  tungsten  lamp  = ,  AC  = ,  BC  = 

.-.  candle  power  of  open  gas  flame  = 

Time  required  to  consume  ^  cu.  ft.  of  gas  =  


[130] 


EXPERIMENT  51  A 


I.  Law  of  inverse  squares,    (a)  Light  the  candle  at  A,  and  one  of  the  group  of  four  candles  at  B, 
in  Fig.  103.   Keep  them  trimmed  so  that  they  burn  as  nearly  as  possible  alike  with  flames  3  cm.  long. 


FIG.  103 

Slide  the  photometer  C  along  the  optical  bench  until  the  spot  or  cross  in  the  photometer  appears 
as  nearly  as  possible  the  same  on  both  sides.  When  in  this  position  the  spot  is  evidently  equally 
illuminated  on  both  sides.  Measure  and  record  the  distances  AC  and  BC.  If  the  optical  bench  has  a 
graduated  bar,  these  distances  may  be  read  directly  on  the  bar. 

(5)  Light  two  of  the  group  of  four  candles  at  B.  See  that  all  three  candles  are  burning  properly, 
Again  slide  the  photometer  C  to  the  position  in  which  it  is  equally  illuminated  on  both  sides.  Measure 
and  record  the  distances  AC  and  BC. 

(<?)  With  three  candles  at  B  lighted,  make  a  similar  set  of  observations. 

(d)  Make  a  fourth  set  of  observations  when  all  four  candles  at  B  are  lighted. 

In  each  of  the  four  cases  above,  compare  the  ratio  of  the  candle  powers  of  the  two  sources  at  A 
and  B  with  the  ratio  of  the  squares  of  their  respective  distances  from  (7,  as  indicated  in  the  data  record. 

State  the  law  which  these  ratios  indicate  must  be  true. 

II.  Replace  the  four  candles  by  a  gas  flame  or  by  an  electric  lamp,  and  find,  with  the  aid  of  the 
law  proved  in  I,  to  how  many  candles  it  is  equivalent ;  that  is,  find  its  candle  power. 

Question.  How  does  the  intensity  of  illumination  on  a  screen  depend  upon  the  distance  when  a  single 
source  of  light  is  placed  at  different  distances  from  the  screen  ? 


AC 

BC 

C.P.  AT  A 

AC2 

C.P.  AT  B 

£C2 

I.  (a) 

1 

1 

(*) 

1 

2 

(<0 

1 

3 

(d) 

1 

4 

II.  C.P.  o 

f  source  at  A  —  1 

AC-  ... 

.  BC-  ... 

.  ...  C.P.  of  ... 

...at£-... 

[131] 


APPENDIX  A 


SUGGESTED  TIME  SCHEDULE  FOR  A  ONE- YEAR  COURSE 


CHAPTER 

SUBJECT 

TIME 

ALLOTTED 

EXPERIMENTS* 
ACCOM  P  AN  Y  ING 

I 

Measurement    

1    week 

1-2 

II 

Pressure  in  Liquids  

li-  weeks 

3-5  A 

III 

Pressure  in  Air     

li  weeks 

6-8 

IV 

Molecular  Motions     

2    weeks 

9-10  A 

v 

Force  and  Motion      

2i  weeks 

11-13 

VI 

Molecular  Forces  

1    week 

14-15 

VII 

Thermometry  ;  Expansion  Coefficients 

1    week 

16-17  A 

VIII 

Work  and  Mechanical  Energy      

2    weeks 

18-20 

IX 

\Vork  and  Heat  Energy      

3    weeks 

21-23 

x 

The  Transference  of  Heat       

i  week 

24 

Review  and  finish  Laboratory  Work     .     .     . 

1    week 

1    week 

XI 

i  week 

25 

XII 

Static  Electricity  

li  weeks 

26-27 

XIII 

Electricity  in  Motion      

2    weeks 

28-31  A 

XIV 

f  Chemical,  Magnetic,  and  Heating"! 
[Effects  of  the  Electric  Current      J 

l£  weeks 

32-34  A 

XV 

Induced  Currents       

2    weeks 

35-37  A 

XVI 

Nature  and  Transmission  of  Sound  .... 

1^  weeks 

38-40 

XVII 

Properties  of  Musical  Sounds       

1£  weeks 

41-42 

XVIII 

Nature  and  Propagation  of  Light     .... 

2    weeks 

48-45 

XIX 

Image  Formation  

2    weeks 

46-48 

XX 

1    week 

49-50 

XXI 

Invisible  Radiations  

^  week 

51  or  51  A 

Review  and  finish  Laboratory  Work     .     .     . 

1    week 

1    week 

Total    

36    weeks 

*  See  Preface  for  the  explanation  of  the  numbering  of  the  experiments  and  the  choices  of  experiments  which  the  system 
of  numbering  suggests. 


[133] 


APPENDIX  B 

RESISTANCES  AND  WEIGHTS*  OF  GERMAN-SILVER  AND  OF  COPPER  WIRE 

BROWN  AND  SHARP  GAUGE 


COPPER  WIRE 

GERMAN-SILVER 
WIRE  (18  %  NICKEL) 

Number 

Diameter  in  mils 
(lmil=  j^in.) 

Ohms  per  1000  ft. 

Pounds  per  1000  ft. 

Ohms  per  1000  ft. 

6 

162. 

.4004 

79. 

7.20 

7 

144. 

.5067 

63. 

9.12 

8 

128. 

.6413 

50. 

11.54 

9 

114. 

.8085 

39. 

14.55 

10 

102. 

1.010 

32. 

18.18 

11 

91.6 

1.269 

25. 

22.84 

12 

80.6 

1.601 

20. 

28.81 

13 

71.8 

2.027 

15.7 

36.48 

14 

64.0 

2.565 

12.4 

46.17 

15 

57.1 

3.234 

9.8 

58.21 

16 

50.8 

4.040 

7.9 

72.72 

17 

45.3 

5.189 

6.1 

93.40 

18 

40.3 

6.567 

4.8 

118.2 

19 

35.9 

8.108 

3.9 

145.9 

20 

32.0 

10.26 

3.1 

184.7 

21 

28.5 

12.94 

2.5 

232.9 

22 

25.3 

16.41 

1.9 

295.4 

23 

22.6 

20.57 

1.5 

370.3 

24 

20.1 

26.01 

1.2 

468.2 

25 

17.9 

32.79 

.97 

590.2 

26 

15.9 

41.56 

.77 

748.1 

27 

14.2 

52.11 

.61 

938.0 

28 

12.6 

66.18  ' 

.48 

1191. 

29 

11.3 

82.29 

.39 

1481. 

30 

10.0 

105.1 

.30 

1892. 

31 

8.93 

132.7 

.24 

2389. 

32 

7.95 

164.2 

.19 

2956. 

33 

7.08 

208.4 

.15 

3751. 

34 

6.30 

264.7 

.12 

4765. 

35 

5.61 

335.1 

.095 

5932. 

36 

5.00 

420.3 

.076 

7565. 

37 

4.45 

530.6 

.060 

9556. 

38 

3.97 

666.7 

.048 

12049. 

39 

3.53 

843.3 

.038 

15431. 

40 

3.14 

1065. 

.030 

19172. 

*  The  weight  per  thousand  feet  of  German-silver  wire  is  about  97  per  cent  of  the  weight  of  copper  wire  of  the  same 
diameter. 

[135] 


ycr 
'  L. 


,.  Mi 


AMfJt. 

UNIVERSITY  OF  CALIFORNIA  LIBRARY 


